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1
XU, Z. S. "CORRELATED LINGUISTIC INFORMATION AGGREGATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 05 (October 2009): 633–47. http://dx.doi.org/10.1142/s0218488509006182.
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Linguistic information aggregation has received great attention from researchers, and a variety of operators have been developed for aggregating linguistic information. All the existing linguistic information aggregation operators only consider the situations where all the aggregated linguistic arguments are independent, i.e., they only consider the addition of the importance of individual linguistic arguments, however, in some actual situations, the considered linguistic arguments may be correlative. In this paper, we focus on this issue. Motivated by the idea of the well-known Choquet integrals,1 we propose two new linguistic information aggregation operators called the linguistic correlated averaging operator and linguistic correlated geometric operator. In the special cases where the aggregated linguistic arguments are independent, the linguistic correlated averaging operator can be reduced to a variety of traditional linguistic averaging aggregation operators; while the linguistic correlated geometric operator can be reduced to a variety of the traditional linguistic geometric aggregation operators. Furthermore, we extend the above results to accommodate uncertain linguistic environments, and illustrate them with a practical problem.
2
YAGER, RONALD R. "CHOQUET AGGREGATION USING ORDER INDUCING VARIABLES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 01 (February 2004): 69–88. http://dx.doi.org/10.1142/s0218488504002667.
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We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation in nearest neighbor methods. We also consider the Choquet aggregation of complex objects such as matrices and vectors.
3
Liu, Peide, Qaisar Khan, Tahir Mahmood, Rashid Ali Khan, and Hidayat Ullah Khan. "Some improved pythagorean fuzzy Dombi power aggregation operators with application in multiple-attribute decision making." Journal of Intelligent & Fuzzy Systems 40, no. 5 (April 22, 2021): 9237–57. http://dx.doi.org/10.3233/jifs-201723.
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Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified.
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Wang, Weize, and Xinwang Liu. "SOME HESITANT FUZZY GEOMETRIC OPERATORS AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING." Technological and Economic Development of Economy 20, no. 3 (June 9, 2014): 371–90. http://dx.doi.org/10.3846/20294913.2013.877094.
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Hesitant fuzzy set (HFS), a generalization of fuzzy set (FS), permits the membership degree of an element of a set to be represented as several possible values between 0 and 1. In this paper, motivated by the extension principle of HFs, we export Einstein operations on FSs to HFs, and develop some new aggregation operators, such as the hesitant fuzzy Einstein weighted geometric operator, hesitant fuzzy Einstein ordered weighted geometric operator, and hesitant fuzzy Einstein hybrid weighted geometric operator, for aggregating hesitant fuzzy elements. In addition, we discuss the correlations between the proposed aggregation operators and the existing ones respectively. Finally, we apply the hesitant fuzzy Einstein weighted geometric operator to multiple attribute group decision making with hesitant fuzzy information. Some numerical examples are given to illustrate the proposed aggregation operators.
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Verma, Rajkumar, and Bhudev Sharma. "Prioritized Information Fusion Method for Triangular Fuzzy Information and Its Application to Multiple Attribute Decision Making." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 02 (April 2016): 265–89. http://dx.doi.org/10.1142/s0218488516500136.
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This study investigates the multiple attribute decision making under triangular fuzzy environment in which the attributes and experts are in different priority level. By combining the idea of quasi arithmetic mean and prioritized weighted average (PWA) operator, we first propose two new prioritized aggregation operators called quasi fuzzy prioritized weighted average (QFPWA) operator and the quasi fuzzy prioritized weighted ordered weighted average (QFPWOWA) operator for aggregating triangular fuzzy information. The properties of the new aggregation operators are studied in detail and their special cases are examined. Furthermore, based on the QFPWA operator and QFPWOWA operator, an approach to deal with multiple attribute decision-making problems under triangular fuzzy environments is developed. Finally, a practical example is provided to illustrate the multiple attribute decision making process.
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Khameneh, Azadeh, and Adem Kiliçman. "m-Polar Fuzzy Soft Weighted Aggregation Operators and Their Applications in Group Decision-Making." Symmetry 10, no. 11 (November 13, 2018): 636. http://dx.doi.org/10.3390/sym10110636.
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Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.
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Wei, Guiwu. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making." International Journal of Decision Support System Technology 10, no. 2 (April 2018): 40–64. http://dx.doi.org/10.4018/ijdsst.2018040103.
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This article utilizes Hamacher operations to develop some uncertain aggregation operators: uncertain Hamacher weighted average (UHWA) operator, uncertain Hamacher weighted geometric (UHWG) operator, uncertain Hamacher ordered weighted average (UHOWA) operator, uncertain Hamacher ordered weighted geometric (UHOWG) operator, uncertain Hamacher hybrid average (UHHA) operator, uncertain Hamacher hybrid geometric (UHHG) operator and some uncertain Hamacher correlate aggregation operators and uncertain induced Hamacher aggregation operators. The prominent characteristics of these proposed operators are studied. Then, the article utilizes these operators to develop some approaches to solve the uncertain multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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SAMINGER, SUSANNE, RADKO MESIAR, and ULRICH BODENHOFER. "DOMINATION OF AGGREGATION OPERATORS AND PRESERVATION OF TRANSITIVITY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, supp01 (December 2002): 11–35. http://dx.doi.org/10.1142/s0218488502001806.
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Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T-transitivity. It will be shown that preservation of T-transitivity is closely related to the domination of the applied aggregation operator over the corresponding t-norm T. Furthermore, basic properties for dominating aggregation operators, not only in the case of dominating some t-norm T, but dominating some arbitrary aggregation operator, will be presented. Domination of isomorphic t-norms and ordinal sums of t-norms will be treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Łukasiewicz t-norm, and the drastic product).
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YANG, WEI. "INDUCED QUASI-ARITHMETIC UNCERTAIN LINGUISTIC AGGREGATION OPERATOR." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, no. 01 (February 2013): 55–77. http://dx.doi.org/10.1142/s0218488513500049.
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Induced quasi-arithmetic aggregation operators are considered to aggregate uncertain linguistic information by using order inducing variables. We introduce the induced correlative uncertain linguistic aggregation operator with Choquet integral and we also present the induced uncertain linguistic aggregation operator by using the Dempster-Shafer theory of evidence. The special cases of the new proposed operators are investigated. Many existing linguistic aggregation operators are special cases of our new operators and more new uncertain linguistic aggregation operators can be derived from them. Decision making methods based on the new aggregation operators are proposed and architecture material supplier selection problems are presented to illustrate the feasibility and efficiency of the new methods.
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Jocic, Dragan, and Ivana Stajner-Papuga. "On distributivity between aggregation operators with annihilator and Mayor’s aggregation operators." Filomat 32, no. 4 (2018): 1475–89. http://dx.doi.org/10.2298/fil1804475j.
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The issue of distributivity for different classes of aggregation operators is a topic that is being currently investigated by a number of researchers. The focus of this paper is on characterization of pairs of aggregation operators that are satisfying distributivity law where one of them is a commutative, associative aggregation operator with annihilator and the other one is a Mayor?s aggregation operator. The results presented here extend and upgrade some known research, e.g., results concerning distributivity between semi-uninorms and Mayor?s aggregation operators.
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Rong, Yuan, Zheng Pei, and Yi Liu. "Hesitant Fuzzy Linguistic Hamy Mean Aggregation Operators and Their Application to Linguistic Multiple Attribute Decision-Making." Mathematical Problems in Engineering 2020 (February 19, 2020): 1–22. http://dx.doi.org/10.1155/2020/3262618.
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Linguistic aggregation operator is a paramount appliance to fix linguistic multiple attribute decision-making (MADM) issues. In the article, the Hamy mean (HM) operator is utilized to fuse hesitant fuzzy linguistic (HFL) information and several novel HFL aggregation operators including the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, weighted hesitant fuzzy linguistic Hamy mean (WHFLHM) operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and weighted hesitant fuzzy linguistic dual Hamy mean (WHFLDHM) operator are proposed. Besides, several paramount theorems and particular cases of these aggregation operators are investigated in detail, and then a novel MADM approach is presented by using the proposed aggregation operators. Ultimately, a practical example is utilized to manifest the effectiveness and practicability of the propounded method.
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Yang, Shanghong, Zhuo Sun, Yanbing Ju, and Chengya Qiao. "A Novel Multiple Attribute Satisfaction Evaluation Approach with Hesitant Intuitionistic Linguistic Fuzzy Information." Mathematical Problems in Engineering 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/692782.
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This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic linguistic fuzzy element (HILFE). Firstly, motivated by the idea of intuitionistic linguistic variables (ILVs) and hesitant fuzzy elements (HFEs), the concept, operational laws, and comparison laws of HILFE are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic linguistic fuzzy information, such as hesitant intuitionistic linguistic fuzzy weighted aggregation operators, hesitant intuitionistic linguistic fuzzy ordered weighted aggregation operators, and generalized hesitant intuitionistic linguistic fuzzy weighted aggregation operators. Moreover, some desirable properties of these operators and the relationships between them are discussed. Based on the hesitant intuitionistic linguistic fuzzy weighted average (HILFWA) operator and the hesitant intuitionistic linguistic fuzzy weighted geometric (HILFWG) operator, an approach for evaluating satisfaction degree is proposed under hesitant intuitionistic linguistic fuzzy environment. Finally, a practical example of satisfaction evaluation for milk products is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.
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Zhang, Chonghui, Weihua Su, Shouzhen Zeng, and Linyun Zhang. "Linguistic Weighted Aggregation under Confidence Levels." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/485923.
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We develop some new linguistic aggregation operators based on confidence levels. Firstly, we introduce the confidence linguistic weighted averaging (CLWA) operator and the confidence linguistic ordered weighted averaging (CLOWA) operator. These two new linguistic aggregation operators are able to consider the confidence level of the aggregated arguments provided by the information providers. We also study some of their properties. Then, based on the generalized means, we introduce the confidence generalized linguistic ordered weighted averaging (CGLOWA) operator. The main advantage of the CGLOWA operator is that it includes a wide range of special cases such as the CLOWA operator, the confidence linguistic ordered weighted quadratic averaging (CLOWQA) operator, and the confidence linguistic ordered weighted geometric (CLOWG) operator. Finally, we develop an application of the new approach in a multicriteria decision-making under linguistic environment and illustrate it with a numerical example.
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Zhao, Shuping, Dong Wang, Changyong Liang, Yajun Leng, and Jian Xu. "Some Single-Valued Neutrosophic Power Heronian Aggregation Operators and Their Application to Multiple-Attribute Group Decision-Making." Symmetry 11, no. 5 (May 10, 2019): 653. http://dx.doi.org/10.3390/sym11050653.
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The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.
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Jin, Min, and Ming-Jing Liao. "Approaches to Multiple Attribute Decision Making Based on the Hesitant Fuzzy Uncertain Linguistic Power Aggregation Operators and Their Applications to Service Quality Evaluation in Higher Education." Journal of Computational and Theoretical Nanoscience 13, no. 10 (October 1, 2016): 7171–75. http://dx.doi.org/10.1166/jctn.2016.5686.
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In this paper, we investigate the multiple attribute decision making problems based on the power aggregation operators with hesitant fuzzy uncertain linguistic information. Then, we have developed some power aggregation operators for aggregating hesitant fuzzy uncertain linguistic information: hesitant fuzzy uncertain linguistic power weighted average (HFULPWA) operator and hesitant fuzzy uncertain linguistic power weighted geometric (HFULPWG) operator. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the service quality in higher education is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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Park, Jin Han, Jung Mi Park, Young Chel Kwun, and Ja Hong Koo. "Induced Power Aggregation Operators and their Applications in Group Decision Making." Applied Mechanics and Materials 404 (September 2013): 672–77. http://dx.doi.org/10.4028/www.scientific.net/amm.404.672.
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The power ordered weighted average (POWA) operator and the power ordered weighted geometric (POWG) operator are the two nonlinear weighted average aggregation tools whose weighting vectors depend on their input arguments. In this paper, as a more general type of POWA and POWG operators, respectively, we develop two induced power aggregation operators called the induced POWA (IPOWA) operator and the induced POWG (IPOWG) operator, respectively, and establish various properties of these induced power aggregation operators, and then apply them, respectively, to develop an approach to multiple attribute group decision making.
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Zahedi Khameneh, Azadeh, and Adem Kilicman. "Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview." Symmetry 12, no. 5 (May 1, 2020): 694. http://dx.doi.org/10.3390/sym12050694.
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Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them.
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Liang, Changyong, Shuping Zhao, and Junling Zhang. "Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems." Foundations of Computing and Decision Sciences 39, no. 3 (July 1, 2014): 189–208. http://dx.doi.org/10.2478/fcds-2014-0011.
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Abstract The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Then, some geometric aggregation operators for aggregating triangular intuitionistic fuzzy numbers are developed, such as triangular intuitionistic fuzzy weighted geometric (TIFWG) operator, the triangular intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator and the triangular intuitionistic fuzzy hybrid geometric (TIFHG) operator. Moreover, an application of the new approach to multi-criteria decision making method was proposed based on the geometric average operator of TIFNs, and the new ranking method for TIFNs is used to rank the alternatives. Finally, an example analysis is given to verify and demonstrate the practicality and effectiveness of the proposed method.
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Khan, Qaisar, Nasruddin Hassan, and Tahir Mahmood. "Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making." Symmetry 10, no. 10 (September 28, 2018): 444. http://dx.doi.org/10.3390/sym10100444.
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The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.
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Luo, Minxia, and Huifeng Long. "Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application." Symmetry 13, no. 1 (January 12, 2021): 119. http://dx.doi.org/10.3390/sym13010119.
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The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.
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Agbodah, Kobina, and Adjei Peter Darko. "Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making." Symmetry 11, no. 1 (January 2, 2019): 39. http://dx.doi.org/10.3390/sym11010039.
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One of the major problems of varied knowledge-based systems has to do with aggregation and fusion. Pang’s probabilistic linguistic term sets denotes aggregation of fuzzy information and it has attracted tremendous interest from researchers recently. The purpose of this article is to deal investigating methods of information aggregation under the probabilistic linguistic environment. In this situation we defined certain Einstein operational laws on probabilistic linguistic term elements (PLTESs) based on Einstein product and Einstein sum. Consequently, we develop some probabilistic linguistic aggregation operators, notably the probabilistic linguistic Einstein average (PLEA) operators, probabilistic linguistic Einstein geometric (PLEG) operators, weighted probabilistic linguistic Einstein average (WPLEA) operators, weighted probabilistic linguistic Einstein geometric (WPLEG) operators. These operators extend the weighted averaging operator and the weighted geometric operator for the purpose of aggregating probabilistic linguistic terms values respectively. Einstein t-norm and Einstein t-conorm constitute effective aggregation tools and they allow input arguments to reinforce each other downwardly and upwardly respectively. We then generate various properties of these operators. With the aid of the WPLEA and WPLEG, we originate the approaches for the application of multiple attribute group decision making (MAGDM) with the probabilistic linguistic term sets (PLTSs). Lastly, we apply an illustrative example to elucidate our proposed methods and also validate their potentials.
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Yang, Wei, Jiarong Shi, and Yongfeng Pang. "Generalized Linguistic Hesitant Intuitionistic Fuzzy Hybrid Aggregation Operators." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/983628.
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Some hybrid aggregation operators have been developed based on linguistic hesitant intuitionistic fuzzy information. The generalized linguistic hesitant intuitionistic fuzzy hybrid weighted averaging (GLHIFHWA) operator and the generalized linguistic hesitant intuitionistic fuzzy hybrid geometric mean (GLHIFHGM) operator are defined. Some special cases of the new aggregation operators are studied and many existing aggregation operators are special cases of the new operators. A new multiple attribute decision making method based on the new aggregation operators is proposed and a practical numerical example is presented to illustrate the feasibility and practical advantages of the new method.
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Yu, Dejian. "Some Generalized Dual Hesistant Fuzzy Geometric Aggregation Operators and Applications." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 03 (June 2014): 367–84. http://dx.doi.org/10.1142/s0218488514500184.
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Information aggregation has been investigated and applied to many fields. This paper focuses on geometric aggregation operators under dual hesitant fuzzy environment. We develop some new geometric aggregation operators, such as the generalized dual hesitant fuzzy weighted geometric (GDHFWG) operator, the generalized dual hesitant fuzzy ordered weighted geometric (GDHFOWG) operator and the generalized dual hesitant fuzzy hybrid geometric (GDHFHG) operator. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of our proposed operators to multi-criteria decision making with dual hesitant fuzzy information, a real decision making problem about human resource generalist selection is forwarded to show the effectiveness of our proposed method.
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Rahman, Khaista, Saleem Abdullah, Asad Ali, and Fazli Amin. "Pythagorean Fuzzy Einstein Hybrid Averaging Aggregation Operator and its Application to Multiple-Attribute Group Decision Making." Journal of Intelligent Systems 29, no. 1 (July 9, 2018): 736–52. http://dx.doi.org/10.1515/jisys-2018-0071.
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Abstract Pythagorean fuzzy set is one of the successful extensions of the intuitionistic fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce the notion of Pythagorean fuzzy Einstein hybrid averaging (PFEHA) aggregation operator along with some of its properties, namely idempotency, boundedness, and monotonicity. PFEHA aggregation operator is the generalization of Pythagorean fuzzy Einstein weighted averaging aggregation operator and Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. The operator proposed in this paper provides more accurate and precise results as compared to the existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator and method to multiple-attribute group decision making.
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Faizi, Shahzad, Wojciech Sałabun, Nisbha Shaheen, Atiq ur Rehman, and Jarosław Wątróbski. "A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment." Mathematics 9, no. 13 (June 24, 2021): 1489. http://dx.doi.org/10.3390/math9131489.
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Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.
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Li, Lifeng, and Qinjun Luo. "Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity." Symmetry 10, no. 12 (December 7, 2018): 729. http://dx.doi.org/10.3390/sym10120729.
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The convexity in triangular norm (for short, ⊗−convexity) is a generalization of Zadeh’s quasiconvexity. The aggregation of two ⊗−convex sets is under the aggregation operator ⊗ is also ⊗−convex, but the aggregation operator ⊗ is not unique. To solve it in complexity, in the present paper, we give some sufficient conditions for aggregation operators preserve ⊗−convexity. In particular, when aggregation operators are triangular norms, we have that several results such as arbitrary triangular norm preserve ⊗ D − convexity and ⊗ a − convexity on bounded lattices, ⊗ M preserves ⊗ H − convexity in the real unite interval [ 0 , 1 ] .
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LIN, JIAN, and QIANG ZHANG. "SOME CONTINUOUS AGGREGATION OPERATORS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATION TO DECISION MAKING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 02 (April 2012): 185–209. http://dx.doi.org/10.1142/s0218488512500092.
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In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.
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RICCI, ROBERTO GHISELLI. "ASYMPTOTICALLY IDEMPOTENT AGGREGATION OPERATORS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 05 (October 2009): 611–31. http://dx.doi.org/10.1142/s0218488509006170.
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This paper deals with aggregation operators. A new form of idempotency, called asymptotic idempotency, is introduced. A critical discussion of the basic notion of aggregation operator, strictly connected with asymptotic idempotency, is provided. Some general construction methods of symmetric, asymptotically idempotent aggregation operators admitting a neutral element are illustrated.
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Park, Jin Han, Jong Jin Seo, Young Chel Kwun, and Ja Hong Koo. "An Approach Based on Power Generalized Aggregation Operator to Decision Making." Advanced Materials Research 542-543 (June 2012): 198–203. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.198.
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The power average (PA) operator and power generalized mean (PGM) operator, proposed by Yager [15], are the nonlinear weighted aggregation tools whose weighting vectors depend on input arguments. In this paper, we study the power generalized mean (PGM) operator and its weighted form, and develop a power ordered weighted generalized mean (POWGM) operator, and study some properties of these operators. The relationship between the PGM operator and other existing operators is also discussed. Moreover, we utilize the weighted PGM operator to develop an approach to group decision making.
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Yang, Wei, Jiarong Shi, Yong Liu, Yongfeng Pang, and Ruiyue Lin. "Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making." Complexity 2018 (November 1, 2018): 1–25. http://dx.doi.org/10.1155/2018/3606245.
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The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.
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Jin, Yun, Hecheng Wu, Jose M. Merigó, and Bo Peng. "Generalized Hamacher Aggregation Operators for Intuitionistic Uncertain Linguistic Sets: Multiple Attribute Group Decision Making Methods." Information 10, no. 6 (June 8, 2019): 206. http://dx.doi.org/10.3390/info10060206.
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In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.
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Wei, Guiwu, and Mao Lu. "Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators in Multiple-Attribute Decision Making." Journal of Intelligent Systems 28, no. 5 (October 17, 2017): 759–76. http://dx.doi.org/10.1515/jisys-2017-0106.
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Abstract The Hamacher product is a t-norm and the Hamacher sum is a t-conorm. They are good alternatives to the algebraic product and the algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average operator, Pythagorean hesitant fuzzy Hamacher weighted geometric operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric operator, Pythagorean hesitant fuzzy Hamacher hybrid average operator, and Pythagorean hesitant fuzzy Hamacher hybrid geometric operator. The prominent characteristics of these proposed operators are studied. Then, we utilize these operators to develop some approaches for solving the Pythagorean hesitant fuzzy multiple-attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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Doncescu, Andrei, Sebastien Regis, Katsumi Inoue, and Richard Emilion. "Analysis of New Aggregation Operators: Mean 3Π." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 6 (July 20, 2007): 561–69. http://dx.doi.org/10.20965/jaciii.2007.p0561.
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Knowledge based systems need to deal with aggregation and fusion of data with uncertainty. To use many sources of information in numerical forms for the purpose of decision or conclusion, systems suppose to have tools able to represent the knowledge in a mathematical form. One of the solutions is to use fuzzy logic operators. We present in this article an improvement of the triple Π operator introduced by Yager and Rybalov, which is calledmean3Π. Whereas triple Π is an operator completely reinforced, the presented operator is a mean operator, which makes it more robust to noise.
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Qin, Yuchu, Xiaolan Cui, Meifa Huang, Yanru Zhong, Zhemin Tang, and Peizhi Shi. "Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making." Complexity 2019 (December 17, 2019): 1–33. http://dx.doi.org/10.1155/2019/3103741.
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q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.
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Akram, Muhammad, Naveed Yaqoob, Ghous Ali, and Wathek Chammam. "Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information." Journal of Mathematics 2020 (August 1, 2020): 1–20. http://dx.doi.org/10.1155/2020/4739567.
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An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.
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Khan, Arshad, Saleem Abdullah, Muhammad Shakeel, Faisal Khan, Noor Amin, and Jianchao Luo. "A New Ranking Methodology for Pythagorean Trapezoidal Uncertain Linguistic Fuzzy Sets Based on Einstein Operations." Symmetry 11, no. 3 (March 25, 2019): 440. http://dx.doi.org/10.3390/sym11030440.
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In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process.
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Zhou, Xiaoqiang, and Qingguo Li. "Multiple Attribute Decision Making Based on Hesitant Fuzzy Einstein Geometric Aggregation Operators." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/745617.
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We first define an accuracy function of hesitant fuzzy elements (HFEs) and develop a new method to compare two HFEs. Then, based on Einstein operators, we give some new operational laws on HFEs and some desirable properties of these operations. We also develop several new hesitant fuzzy aggregation operators, including the hesitant fuzzy Einstein weighted geometric (HFEWGε) operator and the hesitant fuzzy Einstein ordered weighted geometric (HFEWGε) operator, which are the extensions of the weighted geometric operator and the ordered weighted geometric (OWG) operator with hesitant fuzzy information, respectively. Furthermore, we establish the connections between the proposed and the existing hesitant fuzzy aggregation operators and discuss various properties of the proposed operators. Finally, we apply the HFEWGεoperator to solve the hesitant fuzzy decision making problems.
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Qin, Jindong, and Xinwang Liu. "2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection." Kybernetes 45, no. 1 (January 11, 2016): 2–29. http://dx.doi.org/10.1108/k-11-2014-0271.
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Purpose – The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment. Design/methodology/approach – The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (2TLDMM) operator for aggregating the 2-tuple linguistic information, respectively. Some desirable properties and special cases are discussed in detail. Based on which, two approaches to deal with MAGDM problems under 2-tuple linguistic information environment are developed. Finally, a numerical example concerns the supplier selection problem is provided to illustrate the effectiveness and feasibility of the proposed methods. Findings – The results show that the proposed can solve the MAGDM problems within the context of 2-tuple linguistic information, in which the attributes are existing interaction phenomenon. Some 2-tuple aggregation operators based on MM have been developed. A case study of supplier selection is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the linguistic decision information in which the attributes are not independent so as to select the most suitable supplier. Practical implications – The proposed methods can solve the 2-tuple linguistic MAGDM problem, in which the interactions exist among the attributes. Therefore, it can be used to supplier selection problems and other similar management decision problems. Originality/value – The paper develop some 2-tuple aggregation operators based on MM, and further present two methods based on the proposed operators for solving MAGDM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.
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Sang, Xiuzhi, and Xinwang Liu. "Parametric Extension of the Most Preferred OWA Operator and Its Application in Search Engine's Rank." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/273758.
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Most preferred ordered weighted average (MP-OWA) operator is a new kind of neat (dynamic weight) OWA operator in the aggregation operator families. It considers the preferences of all alternatives across the criteria and provides unique aggregation characteristics in decision making. In this paper, we propose the parametric form of the MP-OWA operator to deal with the uncertainty preference information, which includes MP-OWA operator as its special case, and it also includes the most commonly used maximum, minimum, and average aggregation operators. A special form of parametric MP-OWA operator with power function is proposed. Some properties of the parametric MP-OWA operator are provided and the advantages of them in decision making problems are summarized. The new proposed parametric MP-OWA operator can grasp the subtle preference information of the decision maker according to the application context through multiple aggregation results. They are applied to rank search engines considering the relevance of the retrieved queries. An search engine ranking example illustrates the application of parametric MP-OWA operator in various decision situations.
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Lei, Fan, Guiwu Wei, and Xudong Chen. "Some self-evaluation models of enterprise’s credit based on some probabilistic double hierarchy linguistic aggregation operators." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11809–28. http://dx.doi.org/10.3233/jifs-202922.
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Probabilistic double hierarchy linguistic term set (PDHLTS) can not only express the complex linguistic information that the probabilistic linguistic term set (PLTS) cannot express, but also reflect the frequency or importance of linguistic term set (LTS)that cannot be reflected by the double hierarchy linguistic term set (DHLTS). It is an effective tool to deal with multiple attribute group decision making (MAGDM) problems. Therefore, in this paper, we propose several aggregation operators which can aggregate PDHLTS information and apply them to MAGDM problems. Firstly, the basic notion of PDHLTS is reviewed, and the distance formula and algorithm of PDHLTS are defined; then, extant weighted averaging (WA) operator, weighted geometric(WG) operator and power weighted averaging (PWA) operator, power weighted geometric(PWG) operator to PDHLTS, and establish probability double hierarchy linguistic weighted averaging (PDHLWA) operator, probability double hierarchy linguistic weighted geometric (PDHLWG) operator, probability double hierarchy linguistic power weighted averaging (PDHLPWA) operator, probability double hierarchy linguistic power weighted geometric (PDHLPWG) operator; in addition, The idempotency, boundedness and monotonicity of these aggregation operators are studied; what’s more, those aggregation operators are proposed to establish the enterprise credit self-evaluation model; Finally, compared with the available probabilistic double hierarchy linguistic MAGDM methods, the defined model is proved to be scientific and effective.
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Fan, Changxing, and Jun Ye. "Heronian Mean Operator of Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Methods." Mathematical Problems in Engineering 2018 (July 26, 2018): 1–13. http://dx.doi.org/10.1155/2018/4158264.
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Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian mean operator together to develop a LNCN generalized weighted Heronian mean (LNCNGWHM) operator and a LNCN three-parameter weighted Heronian mean (LNCNTPWHM) operator and then discuss their properties. Further, two multiattribute decision methods based on the proposed LNCNGWHM or LNCNTPWHM operator are introduced under LNCN environment. Finally, an example is used to indicate the effectiveness of the developed methods.
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Khan, Majid, Muhammad Gulistan, Naveed Yaqoob, Madad Khan, and Florentin Smarandache. "Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method." Symmetry 11, no. 2 (February 16, 2019): 247. http://dx.doi.org/10.3390/sym11020247.
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Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.
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Waseem, Neha, Muhammad Akram, and José Carlos R. Alcantud. "Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators." Symmetry 11, no. 12 (December 10, 2019): 1498. http://dx.doi.org/10.3390/sym11121498.
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In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.
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He, Yingdong, Zhen He, Panpan Zhou, and Yujia Deng. "Scaled Prioritized Geometric Aggregation Operators and Their Applications to Decision Making." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 01 (February 2016): 13–45. http://dx.doi.org/10.1142/s0218488516500021.
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This paper uses the priority labels to express the detailed prioritized relationship between criteria and develops some scaled prioritized geometric aggregation operators, including the scaled prioritized geometric score (SPGS) operator and the scaled prioritized geometric averaging (SPGA) operator. We also present the uncertain scaled prioritized geometric scoring (USPGS) operator and the uncertain scaled prioritized geometric averaging (USPGA) operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives. The principal advantage of these scaled prioritized geometric aggregation operators is that they are very stable and satisfy monotonicity. Furthermore, we investigate approaches to multi-attribute decision making based on the proposed operators or models and examples are illustrated to show the feasibility and validity of the new approaches. Finally, some further discussions are given.
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Zhao, Shuping, Dong Wang, Liang Changyong, and Wenxing Lu. "Induced Choquet Integral Aggregation Operators with Single-Valued Neutrosophic Uncertain Linguistic Numbers and Their Application in Multiple Attribute Group Decision-Making." Mathematical Problems in Engineering 2019 (February 11, 2019): 1–14. http://dx.doi.org/10.1155/2019/9143624.
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For real decision-making problems, aggregating the attributes which have interactive or correlated characteristics by traditional aggregation operators is unsuitable. Thus, applying Choquet integral operator to approximate and simulate human subjective decision-making process, in which independence among the input arguments is not necessarily assumed, would be suitable. Moreover, using single-valued neutrosophic uncertain linguistic sets (SVNULSs) can express the indeterminate, inconsistent, and incomplete information better than FSs and IFSs. In this paper, we studied the MAGDM problems with SVNULSs and proposed two single-valued neutrosophic uncertain linguistic Choquet integrate aggregation operators where the interactions phenomena among the attributes or the experts are considered. First, the definition, operational rules, and comparison method of single-valued neutrosophic uncertain linguistic numbers (SVNULNs) are introduced briefly. Second, induced single-valued neutrosophic uncertain linguistic Choquet ordered averaging (I-SVNULCA) operator and induced single-valued neutrosophic uncertain linguistic Choquet geometric (I-SVNULCG) operator are presented. Moreover, a few of its properties are discussed. Further, the procedure and algorithm of MAGDM based on the above single-valued neutrosophic uncertain linguistic Choquet integral operator are proposed. Finally, in the illustrative example, the practicality and effectiveness of the proposed method would be demonstrated.
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WANG, JIAN-QIANG, KANG-JIAN LI, and HONG-YU ZHANG. "MULTI-CRITERIA DECISION-MAKING METHOD BASED ON INDUCED INTUITIONISTIC NORMAL FUZZY RELATED AGGREGATION OPERATORS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 04 (August 2012): 559–78. http://dx.doi.org/10.1142/s0218488512500262.
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In this paper, we first defined intuitionistic normal fuzzy numbers as well as their operational laws and score function. Next, we proposed some aggregation operators including ordered intuitionistic normal ordered fuzzy weighted averaging operator, intuitionistic normal fuzzy ordered weighted geometric averaging operator, intuitionistic normal fuzzy related ordered weighted averaging operator, intuitionistic normal fuzzy related ordered weighted geometric averaging operator, induced intuitionistic normal fuzzy related ordered weighted averaging operator and induced intuitionistic normal fuzzy related ordered weighted geometric averaging operator. After that, similarity measure between two intuitionistic normal fuzzy numbers is defined. For multi-criteria decision making problems, in which the criteria are interactive and the criteria values are intuitionistic normal fuzzy numbers, an approach based on induced intuitionistic normal fuzzy related aggregation operators is proposed. And the comprehensive evaluation values of all alternatives can be derived by applying induced intuitionistic normal fuzzy related aggregation operators. Finally, the ranking of the whole alternatives set can be obtained by comparing the relative closeness of alternatives to the ideal solution. In the end, an example is given to show the validity and the feasibility of the method.
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PENG, BO, and CHUNMING YE. "SOME INDUCED UNCERTAIN GEOMETRIC AGGREGATION OPERATORS WITH PURE LINGUISTIC INFORMATION AND THEIR APPLICATION TO GROUP DECISION MAKING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, no. 05 (October 2013): 723–42. http://dx.doi.org/10.1142/s0218488513500347.
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In this paper, we develop some new aggregation operators with pure linguistic information including the uncertain pure linguistic weighted geometric mean (UPLWGM) operator, the induced uncertain pure linguistic ordered weighted geometric mean (IUPLOWGM) operator, and the induced uncertain pure linguistic hybrid geometric mean (IUPLHGM) operator. These developed aggregation operators are very suitable to deal with the situation where the input arguments are represented in uncertain pure linguistic variables. Also, as a more general type of aggregation operator, the IUPLHGM operator is based on the UPLWGM and IUPLOWGM operators, and it can reflect the importance degrees of both the given uncertain linguistic variables and their ordered positions. Moreover, in the situations where the information about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHGM operator for multiple attribute group decision making with pure linguistic information. Finally, an application of the developed approach to group decision making problem regarding the selection of investments is given. Also, we present a comparative analysis with other related decision making methods to demonstrate the effectiveness of the developed approach.
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Khoshaim, Ahmad Bakr, Muhammad Qiyas, Saleem Abdullah, Muhammad Naeem, and Muneeza. "An approach for supplier selection problem based on picture cubic fuzzy aggregation operators." Journal of Intelligent & Fuzzy Systems 40, no. 5 (April 22, 2021): 10145–62. http://dx.doi.org/10.3233/jifs-200194.
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This article is an advanced approach to picture fuzzy set through the application of cubic set theory. For instance, we establish the idea of the picture cubic fuzzy sets (PCFSs) theory and define several operations for PCFS. Also, presented some weighted aggregation operators under picture cubic fuzzy information, so called picture cubic fuzzy weighted averaging (PCFWA) operator, picture cubic fuzzy order weighted averaging (PCFOWA) operator, picture cubic fuzzy weighted geometric (PCFWG) operator, and picture cubic fuzzy order weighted geometric (PCFOWG) operator. Further, we study their fundamental properties and showed the relationship among these aggregation operators. In order to determine the feasibility and practicality of the mentioned new technique, we developed multi-attribute group decision -making algorithm with picture cubic fuzzy environment. Further, the developed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Compared the developed approach with other preexisting aggregation operators, and we concluded that the defined technique is better, reliable and effective.
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Khan, Qaisar, Peide Liu, Tahir Mahmood, Florentin Smarandache, and Kifayat Ullah. "Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making." Symmetry 10, no. 10 (October 2, 2018): 459. http://dx.doi.org/10.3390/sym10100459.
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The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.
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Tan, Chunqiao, and Xiaohong Chen. "Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making." International Journal of Information Technology & Decision Making 15, no. 02 (March 2016): 311–52. http://dx.doi.org/10.1142/s0219622016500048.
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Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.