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Journal articles on the topic 'Aggregation Operator'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

XU, Z. S. "CORRELATED LINGUISTIC INFORMATION AGGREGATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 05 (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 integr

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YAGER, RONALD R. "CHOQUET AGGREGATION USING ORDER INDUCING VARIABLES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 01 (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

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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 (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

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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 (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 be

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Robinson, P. John, and P. Wilson Arul Prakash. "Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems." Indian Journal Of Science And Technology 17, no. 29 (2024): 3026–36. http://dx.doi.org/10.17485/ijst/v17i29.1872.

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Objectives: To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. Methods: A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The proposed improved class of aggregation operators will agg

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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 (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 att

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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 (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 sp

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8

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 (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

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9

Wei, Guiwu. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making." International Journal of Decision Support System Technology 10, no. 2 (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

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10

P, John Robinson, and Wilson Arul Prakash P. "Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems." Indian Journal of Science and Technology 17, no. 29 (2024): 3026–36. https://doi.org/10.17485/IJST/v17i29.1872.

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Abstract <strong>Objectives:</strong> To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. <strong>Methods:</strong> A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The

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11

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 part

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T. Yogashanthi, K. Deva. "A Smart Technique Approach in Picture Fuzzy Schweizer-Sklar Power Geometric Aggregation Operators for Enhancing Road Construction Companies through Group Decision-Making." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2678–95. https://doi.org/10.52783/cana.v32.4548.

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The objective of this paper is to develop picture fuzzy aggregation operators by utilizing the concept of power aggregation operators through Schweizer-Sklar operations. The Schweizer-Sklar t-norm and t-conorm enhance the flexibility of the data integration process and the power aggregation operator, by capturing the interrelationships between various criteria during decision-making. Motivated by Schweizer-Sklar t-norm and t-conorm, this paper aims to develop the theory of the picture fuzzy Schweizer-Sklar power weighted geometric operator and the picture fuzzy Schweizer-Sklar power ordered we

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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 ling

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Selvaraj, Jeevaraj, Prakash Gatiyala, and Sarfaraz Hashemkhani Zolfani. "Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making." Axioms 11, no. 11 (2022): 588. http://dx.doi.org/10.3390/axioms11110588.

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Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decisio

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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 (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.

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16

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 (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. Firs

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17

Qiyas, Muhammad, Talha Madrar, Saifullah Khan, Saleem Abdullah, Thongchai Botmart, and Anuwat Jirawattanapaint. "Decision support system based on fuzzy credibility Dombi aggregation operators and modified TOPSIS method." AIMS Mathematics 7, no. 10 (2022): 19057–82. http://dx.doi.org/10.3934/math.20221047.

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<abstract><p>The operational law plays an important role in the aggregation operator for group decision system. The aggregation information has high influence in aggregating group decision information. Therefore, the main objective of the proposed work is to develop some operational laws as aggregation operator for fuzzy credibility numbers based on Dombi norms. Dombi operations can benefit from the best operational parameter flexibility. To the best of our knowledge, Dombi operations have so far not been used in for fuzzy credibility numbers (FCNs). Using these Dombi t-norm and t-

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18

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 (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

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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 attr

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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 (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

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Tonguc, Tonguc, R. Balaji, Nasreen kausar, and Tonguc Cagin. "The novel algebraic structure trigonometric Pythagorean neutrosophic set provides the basis for interaction weighted aggregating operators." International Journal of Neutrosophic Science 26, no. 1 (2025): 181–91. https://doi.org/10.54216/ijns.260116.

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We introduce new methods for the trigonometric Pythagorean neutrosophic set (TPNSS) via interaction aggregating operator in this study. A combination of the trigonometric operator and the Pythagorean neutrosophic set. The universal aggregation function is used to study the novel averaging and geometric interaction operations of Pythagorean neutrosophic numbers. The TPNSS are commutative, associative, idempotent, and boundedness compatible. TPNSS interaction weighted averaging, TPNSS interaction weighted geometric, generalized TPNSS interaction weighted averaging, and generalized TPNSS interact

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Tonguc, Tonguc, R. Balaji, Nasreen kausar, and Tonguc Cagin. "New form of weighted interaction aggregating operators communicated with the reciprocal fractional floor function via the neutrosophic set." International Journal of Neutrosophic Science 26, no. 1 (2025): 234–42. https://doi.org/10.54216/ijns.260120.

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In this work, we present novel techniques for the reciprocal fractional floor function applied neutrosophic set (RFFFNS) via interaction aggregating operator. The neutrosophic set combined with the reciprocal fractional floor operator. The geometric interaction operations of neutrosophic numbers and their new averaging are studied using the universal aggregation function. The RFFFNS are idempotent, boundedness compatible, commutative, and associative. Four new interaction aggregating operators are introduced: RFFFNS interaction weighted averaging, RFFFNS interaction weighted geometric, general

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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 (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

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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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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 (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) opera

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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 (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 g

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Nur Qafareeny Abdul Halim, Noor Azzah Awang, Siti Nurhidayah Yaacob, Hazwani Hashim, and Lazim Abdullah. "Rough Neutrosophic Shapley Weighted Einstein Averaging Aggregation Operator and its Application in Multi-Criteria Decision-Making Problem." Journal of Advanced Research in Applied Sciences and Engineering Technology 43, no. 2 (2024): 52–64. http://dx.doi.org/10.37934/araset.43.2.5264.

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The study of aggregation operators has played a crucial role in various decision-making methods. The primary function of the aggregation operator is to combine multiple numbers into a single value. While Einstein operators offer a compact notation and can handle complex and large datasets, they do not consider the interaction involved in determining the criteria weights or account for imprecise and indeterminate data. To overcome this limitation, this paper introduces an improved aggregation operator, the rough neutrosophic Shapley weighted Einstein averaging aggregation operator. The rough ne

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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 CGLO

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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 (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 a

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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 numer

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Attaullah, Sultan Alyobi, Mohammed Alharthi, and Yasser Alrashedi. "Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information." Axioms 13, no. 9 (2024): 610. http://dx.doi.org/10.3390/axioms13090610.

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In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hy

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Akram, Muhammad, Rabia Bibi, and Mohammed M. Ali Al-Shamiri. "A Decision-Making Framework Based on 2-Tuple Linguistic Fermatean Fuzzy Hamy Mean Operators." Mathematical Problems in Engineering 2022 (July 6, 2022): 1–29. http://dx.doi.org/10.1155/2022/1501880.

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Aggregation operators are useful tools for approaching situations in the realm of multiattribute decision-making (MADM). Among the most valuable aggregation strategies, the Hamy mean (HM) operator is designed to capture the correlations among integral parameters. In this article, a series of Hamy-inspired operators are used to combine 2-tuple linguistic Fermatean fuzzy (2TLFF) information. The new 2TLFF aggregation operators that are born from this adaptation include the 2-tuple linguistic Fermatean fuzzy Hamy mean (2TLFFHM) operator, 2-tuple linguistic Fermatean fuzzy weighted Hamy mean (2TFF

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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 (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-

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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 (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 pape

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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 (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

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Li, Lifeng, and Qinjun Luo. "Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity." Symmetry 10, no. 12 (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

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Deva, Krishnan, and Swaminathan Mohanaselvi. "Picture Fuzzy Choquet Integral Based Geometric Aggregation Operators and Its Application to Multi Attribute Decision-Making." Mathematical Modelling of Engineering Problems 9, no. 4 (2022): 1043–52. http://dx.doi.org/10.18280/mmep.090422.

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Picture fuzzy set is an extension of intuitionistic fuzzy set, which allows interpreting uncertain data in decision-making problems. This study provides aggregation operators based on Choquet integral, namely Choquet integral picture fuzzy geometric aggregation (CIPFGA) operator and Choquet integral picture fuzzy hybrid geometric aggregation (CIPFHGA) operator with certain properties of these operators are established. We validate the functioning of the operators with illustrative examples. The CIPFHGA operator has an added benefit of combining the weights of positions along with capturing the

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Riaz, Muhammad, and Hafiz Muhammad Athar Farid. "Picture fuzzy aggregation approach with application to third-party logistic provider selection process." Reports in Mechanical Engineering 3, no. 1 (2022): 318–27. http://dx.doi.org/10.31181/rme20023062022r.

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Picture fuzzy sets (PFSs) are frequently composed of positive, neutral, and negative memberships and have the benefit of precisely capturing the preferences of decision makers (DMs). This paper introduces innovative picture fuzzy aggregation operators (AOs) based on fundamental operations, which have a number of advantages when dealing with real-world scenarios. Unpredictability and fuzziness coexist in decision-making analysis due to the complexity of the decision-making environment. ”Picture fuzzy numbers” (PFNs) outperform ”intuitionistic fuzzy numbers” (IFNs) when dealing with unclear inpu

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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 (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 ge

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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 geometri

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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 (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 deci

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Shit, Chittaranjan, Ganesh Ghorai, Qin Xin, and Muhammad Gulzar. "Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem." Symmetry 14, no. 1 (2022): 135. http://dx.doi.org/10.3390/sym14010135.

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Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator

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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) ope

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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 (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 g

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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 (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

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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

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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 multi

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RICCI, ROBERTO GHISELLI. "ASYMPTOTICALLY IDEMPOTENT AGGREGATION OPERATORS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 05 (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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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 (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 PD

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Wang, Yong-Long, Ebenezer Bonyah, Mashael Khayyat, Zubair Ahmad, Muhammad Shakeel, and Waris Khan. "A Novel Approach on Decision Support System Based on the Aczel-Alsina Aggregation Operators and Their Applications to Supplier Selection Problems." Journal of Function Spaces 2022 (December 28, 2022): 1–26. http://dx.doi.org/10.1155/2022/2557309.

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Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types of induced aggregation operators, based on the Aczel-Alsina operations. We construct some induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina ordered weighted averaging/geometric (I-IVITrFAAOWA/G) operator, induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina hybrid averaging/geometric (I-IVITrFAAHA/G) operator. Moreover, some dominant properties of

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