Journal articles: 'Ranking triangular fuzzy numbers'

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Facchinetti, Gisella, Roberto Ghiselli Ricci, and Silvia Muzzioli. "Note on ranking fuzzy triangular numbers." International Journal of Intelligent Systems 13, no. 7 (July 1998): 613–22. http://dx.doi.org/10.1002/(sici)1098-111x(199807)13:7<613::aid-int2>3.0.co;2-n.

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Tang, Hui-Chin, Tien-Lin Chao, and Kuang-Hang Hsieh. "A weighted ranking function for ranking triangular fuzzy numbers." Journal of Information and Optimization Sciences 33, no. 1 (January 2012): 149–58. http://dx.doi.org/10.1080/02522667.2012.10700140.

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AKYAR, EMRAH, HANDAN AKYAR, and SERKAN ALİ DÜZCE. "A NEW METHOD FOR RANKING TRIANGULAR FUZZY NUMBERS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 05 (October 2012): 729–40. http://dx.doi.org/10.1142/s021848851250033x.

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The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

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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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John Robinson P. "Multiple Attribute Group Decision Analysis for Intuitionistic Triangular and Trapezoidal Fuzzy Numbers." International Journal of Fuzzy System Applications 5, no. 3 (July 2016): 42–76. http://dx.doi.org/10.4018/ijfsa.2016070104.

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Solving Multiple Attribute Group Decision Making (MAGDM) problems has become one of the most important researches in recent days. In situations where the information or the data is of the form of an Intuitionistic Triangular Fuzzy Number (ITrFN) or Intuitionistic Trapezoidal Fuzzy Number (ITzFN), a new distance function is defined for ranking the alternatives in the decision making process. After processing the decision information through a sequence of arithmetic aggregation operators, namely, the Intuitionistic Triangular Fuzzy Weighted Arithmetic Averaging (ITrFWAA), Intuitionistic Triangular Fuzzy Ordered Weighted Averaging (ITrFOWA) operator and the Intuitionistic Triangular Fuzzy Hybrid Aggregation (ITrFHA) operator, the proposed distance function is utilized to rank the best alternative. A model is proposed to solve MAGDM problems using the developed distance formula defined for ITrFNs. Numerical illustration is provided and comparisons are made with some of the existing MAGDM models and ranking procedures.

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Atalik, Gultekin, and Sevil Senturk. "A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 6271–78. http://dx.doi.org/10.3233/jifs-189095.

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Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

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Mohammed Ramadan, Ayad. "Ranking of Fuzzy Numbers by using Scaling Method." passer 3, no. 2 (2019): 137–43. http://dx.doi.org/10.24271/psr.24.

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In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers

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Akyar, Handan. "Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/3080679.

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Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach.

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Rao, P. Phani Bushan, and N. Ravi Shankar. "Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality." Advances in Fuzzy Systems 2011 (2011): 1–7. http://dx.doi.org/10.1155/2011/178308.

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Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.

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Nguyen, Thanh-Lam. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews." Complexity 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3083745.

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Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.

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Dai, Wen-feng, Qiu-yan Zhong, and Chun-ze Qi. "Multistage Multiattribute Group Decision-Making Method Based on Triangular Fuzzy MULTIMOORA." Mathematical Problems in Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/1687068.

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This paper proposed a new multiattribute group decision-making method, in which the period significance coefficients and the attribute significance coefficients are completely unknown, and the attribute values are triangular fuzzy numbers. At first, to obtain the period significance coefficients, the period significance coefficients optimization model is constructed according to the time degree and the differences of the decision information in different periods. Then, attribute significance coefficients are determined by the maximum deviation method. Based on this, alternatives are ranked by the triangular fuzzy ratio system method, the triangular fuzzy reference point method, and the triangular fuzzy full multiplicative form, respectively. The dominance theory is used for aggregating the subordinate rankings into the final ranking. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed method.

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Mandal, Nirmal. "Fuzzy economic order quantity model with ranking fuzzy number cost parameters." Yugoslav Journal of Operations Research 22, no. 2 (2012): 247–64. http://dx.doi.org/10.2298/yjor110727014m.

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In this paper, a multi-objective economic order quantity model with shortages and demand dependent unit cost under storage space constraint is formulated. In real life situation, the objective and constraint goals and cost parameters are not precisely defined. These are defined in fuzzy environment. The cost parameters are represented here as triangular shaped fuzzy numbers with different types of left and right branch membership functions. The fuzzy numbers are then expressed as ranking fuzzy numbers with best approximation interval. Geometric programming approach is applied to derive the optimal decisions in closed form. The inventory problem without shortages is discussed as a special case of the original problem. A numerical illustration is given to support the problem.

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Zhou, Hui, and Haiping Ren. "A novel ranking function-based triangular intuitionistic fuzzy fault tree analysis method." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 2753–61. http://dx.doi.org/10.3233/jifs-191018.

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In reliability field, the probabilities of basic events are often treated as exact values in conventional fault tree analysis. However, for many practical systems, because the concept of events may be ambiguous, the factors affecting the occurrence of events are complex and changeable, so it is difficult to obtain accurate values of the occurrence probability of events. Fuzzy sets can well deal with these situations. Thus this paper will develop a novel fault tree analysis method in the assumption of the values of probability of basic events expressed with triangular intuitionistic fuzzy numbers. First, a new ranking function of triangular intuitionistic numbers is established, which can reflect the behavior factors of the decision maker. Then a novel fault tree analysis method is put forward on the basis of operational laws and the proposed ranking function of triangular intuitionistic numbers. Finally, an example of weapon system “automatic gun” is employed to show that the proposed fault tree analysis method is feasible and effective.

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Sotoudeh-Anvari, Alireza. "A necessary condition for comparing and ranking of triangular fuzzy numbers on the basis of height-independent ranking techniques." International Journal of Knowledge-based and Intelligent Engineering Systems 24, no. 4 (January 18, 2021): 269–77. http://dx.doi.org/10.3233/kes-180163.

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The open problem of comparing fuzzy numbers as one of the most important issues in fuzzy sets has been studied by many researchers. However, this problem has not been solved up to now and perhaps it will never be fully answered. This work proposes a necessary condition for ranking of triangular fuzzy numbers on the basis of some efficient height-independent ranking methods such as centroids, total integral value, signed distance and defuzzification. To the best of our knowledge, this paper provides the first use of a necessary condition in ranking methods. Fortunately, suggested approach is very straightforward, fast and efficient to use in the real problems. To evaluate the suggested approach with the result of existing methods, six examples are presented. Finally, we apply this necessary condition for ranking fuzzy numbers to a fuzzy failure mode and effect analysis (FMEA) problem. The results show that our approach is practical and has reasonable outcome.

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Zou, Shu-Cai, Fang Liu, and Qi-Rui You. "A Two-Dimensional Simulation Approach for Ranking Fuzzy Numbers by the Monte Carlo Technique." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 04 (August 2021): 559–86. http://dx.doi.org/10.1142/s0218488521500240.

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The ranking of fuzzy numbers has an important position in fuzzy application models and systems. In this paper, a two-dimensional approach is proposed by the Monte Carlo simulation technique, and the simulation formula of the possibility degree is established. The algorithms for ranking interval numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers are elaborated on. Moreover, the axiomatic properties of the possibility degree formulae are investigated. It is found that the simulation formula of the possibility degree is reasonable for the satisfaction of the considered axiomatic properties. Finally, by considering a set of fuzzy numbers and the effect of a viewpoint, some comparisons are reported by carrying out numerical examples. The observations reveal that the proposed simulation method is effective to reflect the uncertainty of fuzzy numbers and coherent with the human intuition.

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RICCI, ROBERTO GHISELLI. "AN AXIOMATIC APPROACH TO A CLASS OF RANKING FUNCTIONS FOR TRIANGULAR FUZZY NUMBERS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, no. 02 (April 1999): 155–72. http://dx.doi.org/10.1142/s0218488599000106.

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This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision-making situations. A new approach is followed through the definition of some axiomatic requirements which represent the essential properties that characterize an arbitrary ranking function. A notion of degree of risk associated to every ranking function is proposed to discriminate equivalent alternatives.

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Narayanamoorthy, S., and S. Maheswari. "The Intelligence of Octagonal Fuzzy Number to Determine the Fuzzy Critical Path: A New Ranking Method." Scientific Programming 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/6158208.

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This research paper proposes a modified ranking approach to determine the critical path in fuzzy project network, where the duration of each activity time is represented by an octagonal fuzzy number. In this method, a modified subtraction formula is carried out on fuzzy numbers. This modified method works well on fuzzy backward pass calculations as there will be no negative time. The analysis is expected to show that the fuzzy number which is used in this paper is more effective in determining the critical path in a fuzzy project network and possibility of meeting the project time. A numerical example is given and compared with trapezoidal, triangular fuzzy numbers through proposed ranking method.

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Gotmare, Anil. "Solution of a Fuzzy Assignment Problem by using Branch-and-Bound Technique with application of linguistic variable." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 15, no. 4 (February 10, 2016): 6649–53. http://dx.doi.org/10.24297/ijct.v15i4.548.

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In this paper Branch and bound technique is applied to assignment problem with fuzzy cost with objective to minimise cost, fuzzy cost is assumed as triangular fuzzy number, Yagerâ€™s ranking method has been used for ranking the fuzzy numbers, after transforming assignment problem into a crisp one using linguistic variables, assignment problem is solved by branch and bound technique. To deal with fuzzy assignment problem with qualitative data, linguistic variable helps to convert qualitative data into quantitative data.

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Roldán López de Hierro, Antonio Francisco, Miguel Sánchez, Daniel Puente-Fernández, Rafael Montoya-Juárez, and Concepción Roldán. "A Fuzzy Delphi Consensus Methodology Based on a Fuzzy Ranking." Mathematics 9, no. 18 (September 19, 2021): 2323. http://dx.doi.org/10.3390/math9182323.

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Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts’ subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert’s fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts’ answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers.

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SIGARPICH, LEILA ALIZADEH, TOFIGH ALLAHVIRANLOO, FARHAD HOSSEINZADEH LOTFI, and NARSIS AFTAB KIANI. "DEGENERACY IN FUZZY LINEAR PROGRAMMING AND ITS APPLICATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 06 (December 2011): 999–1012. http://dx.doi.org/10.1142/s021848851100743x.

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In this paper, by a definite linear function for ranking symmetric triangular fuzzy numbers, in a Fuzzy Linear Programming problem (FLP) model, we introduced a Fuzzy Degenerate Solution (FDS). In the physical meaning, occurrence of degeneracy in a Fuzzy Minimal Cost Flow Network is investigated. To prevent of falling into Cycling phenomenon in optimization process, we defined two new techniques of Cycling prevention proper to fuzzy environment.

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Kosareva, Natalja, and Aleksandras Krylovas. "COMPARISON OF ACCURACY IN RANKING ALTERNATIVES PERFORMING GENERALIZED FUZZY AVERAGE FUNCTIONS." Technological and Economic Development of Economy 19, no. 1 (April 2, 2013): 162–87. http://dx.doi.org/10.3846/20294913.2012.763072.

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The paper defines the notions of point, interval and triangular intuitionistic fuzzy numbers expressing the degree of membership and non-membership in the fuzzy set. The generalized fuzzy weighted average function is introduced according to operation rules on intuitionistic fuzzy numbers. In special cases, the generalized weighted average coincides with an arithmetic average or a geometric average. The generalized fuzzy weighted average function could be applied for solving problems in multiple criteria decision making. Research on the stability of the generalized weighted averaging operator of ranking alternatives was performed applying the Monte Carlo method. The aim of the conducted research is to establish the types of intuitionistic fuzzy numbers and the exponent values of the generalized weighted averaging operator having the least error probabilities considering alternatives ranking. Computations were performed involving 3, 4 and 5 experts. In the case of 5 experts, initial decision matrices having high, middle and low separability alternatives were examined. Decision matrices created by the experts were modelled generating random intuitionistic fuzzy numbers according to uniform and normal distribution. The example of applying such methodology was shown to solve a real problem of ranking possible redevelopment alternatives for derelict rural buildings.

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Li, Tiejun, Jianhua Jin, and Chunquan Li. "Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers." Journal of Applied Mathematics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/304287.

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Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.

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Poonam, Shugani. "Fuzzy Transportation Problem of Triangular Numbers with 𝜶 −Cut and Ranking Technique." IOSR Journal of Engineering 02, no. 05 (May 2012): 1162–64. http://dx.doi.org/10.9790/3021-020511621164.

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Niksirat, Malihe, and Hadi Nasseri. "Knapsack problem in fuzzy nature: Different models based on credibility ranking method." Yugoslav Journal of Operations Research, no. 00 (2021): 21. http://dx.doi.org/10.2298/yjor210219021n.

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This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for fuzzy knapsack problem are proposed including, expected value model, chance-constrained model, and dependent-chance model. Credibility ranking method is applied to convert the fuzzy models into a crisp equivalent linear one considering triangular and trapezoidal fuzzy numbers. The solution of the fuzzy problem is obtained with respect to different satisfaction degrees in the objective function and constraints. Several numerical examples are given to demonstrate different models and concepts. The proposed approaches are applied to model and to solve a fuzzy pre-disaster investment decision problem.

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Aikhuele, Daniel Osezua. "Aggregating and Ranking Method for the Evaluation of Product Design Materials." International Journal of Operations Research and Information Systems 10, no. 4 (October 2019): 39–52. http://dx.doi.org/10.4018/ijoris.2019100103.

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A new MCDM model based on a triangular intuitionistic fuzzy (TIF) aggregating and ranking model is proposed for the evaluation of adhesive materials used in joining fibre-reinforced plastic. The new model which uses the triangular intuitionistic fuzzy numbers (TIFN), TIF aggregating operators and the TIF ranking functions provides a more accurate method for assessing uncertain or imprecise information in the decision-making process. The model addresses the MCDM problem in which the available information cannot be assessed with exact numbers and requires the use of a more holistic approach which is a drawback in the existing MCDM methods used in the evaluation of design materials in literature. The result from the evaluation shows that the alternative T3 (Polyurethane) has the best chances of been used in joining the FRP with respect to the fracture mechanics-based criteria. With the ranking result presented, the study can conclude that the procedure used for the evaluation of the adhesive material has led to the selection of the best adhesive material for joining the FRP elements.

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Hadikurniawati, Wiwien, and Khabib Mustofa. "Multicriteria Group Decision Making Using Fuzzy Approach for Evaluating Criteria of Electrician." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 5 (October 1, 2016): 2462. http://dx.doi.org/10.11591/ijece.v6i5.10946.

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<p>This paper presents an approach of fuzzy multicriteria group decision making in determining alternatives to solve the selection problem of the electrician through a competency test. Fuzzy approach is used to determine the highest priority of alternative electrician who has knowledge and ability that best fits the given parameters. Linguistic variables are presented by triangular fuzzy numbers. They are used to represent a subjective assessment of the decision-makers so that uncertainty and imprecision in the selection process can be minimized. Fuzzy approach require transforming crisp data to fuzzy numbers. Output of the best alternatives is generated by ranking method. Ranking has been made base on eight criteria which make the evaluation basis of each alternative. Ranking of the results is determined using different value of optimism index (). The fuzzy multi criteria decision making (FMCDM) calculation is using the best alternative using three value of optimism index. The result of calculation shows that the same alternative reached from different index of optimism. This alternative is the highest priority of decision making process.</p>

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Hadikurniawati, Wiwien, and Khabib Mustofa. "Multicriteria Group Decision Making Using Fuzzy Approach for Evaluating Criteria of Electrician." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 5 (October 1, 2016): 2462. http://dx.doi.org/10.11591/ijece.v6i5.pp2462-2469.

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<p>This paper presents an approach of fuzzy multicriteria group decision making in determining alternatives to solve the selection problem of the electrician through a competency test. Fuzzy approach is used to determine the highest priority of alternative electrician who has knowledge and ability that best fits the given parameters. Linguistic variables are presented by triangular fuzzy numbers. They are used to represent a subjective assessment of the decision-makers so that uncertainty and imprecision in the selection process can be minimized. Fuzzy approach require transforming crisp data to fuzzy numbers. Output of the best alternatives is generated by ranking method. Ranking has been made base on eight criteria which make the evaluation basis of each alternative. Ranking of the results is determined using different value of optimism index (). The fuzzy multi criteria decision making (FMCDM) calculation is using the best alternative using three value of optimism index. The result of calculation shows that the same alternative reached from different index of optimism. This alternative is the highest priority of decision making process.</p>

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Et. al., K. Selvakumari,. "Analysis of Fuzzy Non-preemptive Priority Queuing Model with Unequal Service Rate." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 1457–60. http://dx.doi.org/10.17762/turcomat.v12i5.2110.

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This article provides an effective method to analyze the performance measures of non-preemptive fuzzy priority queues with unequal service rates. Here the arrival rate and the service rate are in fuzzy numbers. Using a new ranking method, the fuzzy values are reduced to the crisp values. For that cause, both the Triangular Fuzzy Number (TFN) and Trapezoidal Fuzzy Number (TpFN) are chosen to establish the proposal's effectiveness. An illustration is given to find the efficiency of the performance measures of the fuzzy queuing model.

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Krylovas, Aleksandras, and Natalja Kosareva. "EXPERT ESTIMATES AVERAGING BY CONSTRUCTING INTUITIONISTIC FUZZY TRIANGLES." Mathematical Modelling and Analysis 20, no. 3 (June 2, 2015): 409–21. http://dx.doi.org/10.3846/13926292.2015.1049970.

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The problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with different uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision probability matrices is proposed in the paper. Ranking results obtained by performing Monte Carlo simulations. Probabilities of errors are compared for arithmetic, geometric, fuzzy arithmetic and fuzzy geometric averages.

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Wang, Xingang, and Ke Wang. "A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method." Journal of Intelligent & Fuzzy Systems 40, no. 1 (January 4, 2021): 221–33. http://dx.doi.org/10.3233/jifs-191261.

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In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.

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Li, Deng Feng, Juang Xia Nan, and Mao Jun Zhang. "A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making." International Journal of Computational Intelligence Systems 3, no. 5 (2010): 522. http://dx.doi.org/10.2991/ijcis.2010.3.5.2.

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Li, Deng Feng, Jiang Xia Nan, and Mao Jun Zhang. "A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making." International Journal of Computational Intelligence Systems 3, no. 5 (October 2010): 522–30. http://dx.doi.org/10.1080/18756891.2010.9727719.

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Facchinetti, Gisella, and Roberto Ghiselli Ricci. "A characterization of a general class of ranking functions on triangular fuzzy numbers." Fuzzy Sets and Systems 146, no. 2 (September 2004): 297–312. http://dx.doi.org/10.1016/j.fss.2003.10.023.

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Srinivasan, A., and G. Geetharamani. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints." Journal of Applied Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/8496812.

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Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

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OPRICOVIC, SERAFIM. "A FUZZY COMPROMISE SOLUTION FOR MULTICRITERIA PROBLEMS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 03 (June 2007): 363–80. http://dx.doi.org/10.1142/s0218488507004728.

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The VIKOR-F method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. It determines the compromise solution that is the "closest" to the ideal. Imprecision in multicriteria decision making can be modelled using fuzzy set theory to define criteria and the importance of criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. It is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the VIKOR-F algorithm. A numerical example illustrates an application of the VIKOR-F method.

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Liu, Yujia, Jian Wu, and Changyong Liang. "Attitudinal ranking and correlated aggregating methods for multiple attribute group decision making with triangular intuitionistic fuzzy Choquet integral." Kybernetes 44, no. 10 (November 2, 2015): 1437–54. http://dx.doi.org/10.1108/k-02-2014-0040.

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Purpose – The purpose of this paper is to propose novel attitudinal prioritization and correlated aggregating methods for multiple attribute group decision making (MAGDM) with triangular intuitionistic fuzzy Choquet integral. Design/methodology/approach – Based on the continuous ordered weighted average (COWA) operator, the triangular fuzzy COWA (TF-COWA) operator is defined, and then a novel attitudinal expected score function for triangular intuitionistic fuzzy numbers (TIFNs) is investigated. The novelty of this function is that it allows the prioritization of TIFNs by taking account of the expert’s attitudinal character. When the ranking order of TIFNs is determined, the triangular intuitionistic fuzzy correlated geometric (TIFCG) operator and the induced TIFCG (I-TIFCG) operator are developed. Findings – Their use is twofold: first, the TIFCG operator is used to aggregate the correlative attribute value; and second, the I-TIFCG operator is designed to aggregate the preferences of experts with some degree of inter-dependent. Then, a TIFCG and I-TIFCG operators-based approach is presented for correlative MAGDM problems. Finally, the propose method is applied to select investment projects. Originality/value – Based on the TIFCG and I-TIFCG operators, this paper proposes a novel correlated aggregating methods for MAGDM with triangular intuitionistic fuzzy Choquet integral. This method helps to solve the correlated attribute (criteria) relationship. Furthermore, by the attitudinal expected score functions of TIFNs, the propose method can reflect decision maker’s risk attitude in the final decision result.

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Dong, Jiuying, and Shuping Wan. "A new method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers." Kybernetes 45, no. 1 (January 11, 2016): 158–80. http://dx.doi.org/10.1108/k-02-2015-0058.

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Purpose – The triangular intuitionistic fuzzy number (TIFN) is very useful for expressing ill-known quantity. The purpose of this paper is to develop a new method for multi-attribute group decision-making (MAGDM) problems, in which the attribute values are the TIFNs, the attribute weights are completely unknown and the weights of decision makers are given by linguistic variables. Design/methodology/approach – A new method is given to rank TIFNs based on the weighted possibility mean and standard deviation of TIFNs. The weighted Minkowski distance of TIFNs is defined by using the weighted lower and upper possibility means of TIFNs. The weights of experts are determined in terms of the voting model of intuitionistic fuzzy set (IFS). The weights of attributes can be objectively determined through utilizing the information entropy defined by weighted Minkowski distance of TIFNs. Through integrating the attribute weights and expert weights, the collective comprehensive ranking values of alternatives are obtained and used to rank the alternatives. Findings – The stock selection example and comparison analysis show the validity and applicability of the method proposed in this paper. Originality/value – The paper presents a new ranking method of TIFNs and defines the weighted Minkowski distance of TIFNs. The weights of experts are determined in terms of the voting model of IFS. The weights of attributes can be objectively determined through utilizing the information entropy. The proposed method can greatly enhance the flexibility and agility of decision-making process.

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Milošević, Mimica R., Dušan M. Milošević, Ana D. Stanojević, Dragan M. Stević, and Dušan J. Simjanović. "Fuzzy and Interval AHP Approaches in Sustainable Management for the Architectural Heritage in Smart Cities." Mathematics 9, no. 4 (February 4, 2021): 304. http://dx.doi.org/10.3390/math9040304.

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For the past four decades, the methodology of fuzzy analytic hierarchy process based on fuzzy trapezoidal or triangular numbers with the linear type of membership functions has witnessed an expanding development with applicability to a wide variety of areas, such as industry, environment, education, government, economics, engineering, health, and smart city leadership. On the other hand, the interval gray analytic hierarchy process is a more practical method when a significant number of professionals have large variations in preferences and interests in complex decisions. The paper examines the management of architectural heritage in smart cities, using methods of multi-criteria decision making. Two appropriate methods generally recommended by the scientific literature have been applied: fuzzy and interval grey analytic hierarchy process. By using both techniques, there is an opportunity to analyze the consensual results from the aspect of two different stakeholder groups: architectural heritage experts and smart city development experts. Trapezoidal fuzzy analytical hierarchical process shows better stability than a triangular one. Both approaches assign priority to the strategy, but the interval approach gives a more significant rank to architectural heritage factors. The similarity of the proposed methods has been tested, and the similarity factor in the ranking indicates a high degree of similarity in comparing the reference rankings.

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Srivastava, Pankaj Kumar, and Dinesh C. S. Bisht. "Dichotomized Incenter Fuzzy Triangular Ranking Approach to Optimize Interval Data Based Transportation Problem." Cybernetics and Information Technologies 18, no. 4 (November 1, 2018): 111–19. http://dx.doi.org/10.2478/cait-2018-0051.

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Abstract This research article discusses the problems having flexible demand, supply and cost in range referred as interval data based transportation problems and these cannot be solved directly using available methods. The uncertainty associated with these types of problems motivates authors to tackle it by converting interval to fuzzy numbers. This confront of conversion has been achieved by proposing a dichotomic fuzzification approach followed by a unique triangular incenter ranking approach to optimize interval data based transportation problems. A comparison with existing methods is made with the help of numerical illustrations. The algorithm proposed is found prompt in terms of the number of iteration involved and problem formation. This method is practical to handle the transportation problems not having a single valued data, but data in form of a range.

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Li, Deng-Feng. "A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems." Computers & Mathematics with Applications 60, no. 6 (September 2010): 1557–70. http://dx.doi.org/10.1016/j.camwa.2010.06.039.

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Mondal, Sankar Prasad, Adrijit Goswami, and Sujit Kumar De. "Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation." Advances in Fuzzy Systems 2019 (March 3, 2019): 1–14. http://dx.doi.org/10.1155/2019/4142382.

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In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). All the arithmetic operations are done by max-min principle method which is nothing but the application of interval analysis. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy number. The de-i-fuzzification of the corresponding intuitionistic fuzzy solution is done by average of (α,β)-cut method. Finally we solve integral equation with NIFN by the help of intuitionistic fuzzy Laplace transform method.

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Jakšić, Milena, Slaviša Moljević, Aleksandar Aleksić, Mirjana Misita, Slavko Arsovski, Danijela Tadić, and Predrag Mimović. "Fuzzy Approach in Ranking of Banks according to Financial Performances." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/6169586.

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Evaluating bank performance on a yearly basis and making comparison among banks in certain time intervals provide an insight into general financial state of banks and their relative position with respect to the environment (creditors, investors, and stakeholders). The aim of this study is to propose a new fuzzy multicriteria model to evaluate banks respecting relative importance of financial performances and their values. The relative importance of each pair of financial performance groups is assessed linguistic expressions which are modeled by triangular fuzzy numbers. Fuzzy Analytic Hierarchical Process (FAHP) is applied to determine relative weights of the financial performances. In order to rank the treated banks, new model based on Fuzzy Technique for Order Performance by Similarity to Ideal Solution (FTOPSIS) is deployed. The proposed model is illustrated by an example giving real life data from 12 banks having 80% share of the Serbian market. In order to verify the proposed FTOPSIS different measures of separation are used. The presented solution enables the ranking of banks, gives an insight of bank’s state to stakeholders, and provides base for successful improvement in a field of strategy quality in bank business.

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Arya, Alka, and Shiv Prasad Yadav. "Performance Efficiency of Public Health Sector Using Intuitionistic Fuzzy DEA." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 02 (April 2020): 289–315. http://dx.doi.org/10.1142/s0218488520500129.

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Out of several generalizations of fuzzy set theory for various objectives, the notions of intuitionistic fuzzy sets (IFSs) is very useful in modeling real life problems. In existing fuzzy data envelopment analysis (FDEA) models, the inputs and outputs are limited to fuzzy input and fuzzy output data. In real life problems, the input data and output data can be considered as linguistic/vague characterized by intuitionistic fuzzy numbers (IFNs). So, in the present study, we extend FDEA to intuitionistic FDEA (IFDEA) in which the input and output data are taken as IFNs, in particular triangular IFNs (TIFNs). In this study, we develop models to measure the efficiencies of each DMU in intuitionistic fuzzy environment using α and β-cuts and we get IF interval efficiencies. The ranking of FNs has been studied by many authors and extended to IFNs because of its applicability in real life problems. The ranking of IF interval efficiency plays an important role in DEA where the interval analysis is essential. Further, in this paper a new method for ranking IF interval efficiencies has been proposed and compared with other existing methods. A new general minimax approach is proposed to compare and rank the IF efficiency intervals of DMUs. One numerical example is provided to show the applications of the proposed IFDEA model and the proposed ranking approach. Moreover, we present an application of the proposed approach to the public health sector.

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Turskis, Zenonas, and Edmundas Kazimieras Zavadskas. "A NEW FUZZY ADDITIVE RATIO ASSESSMENT METHOD (ARAS‐F). CASE STUDY: THE ANALYSIS OF FUZZY MULTIPLE CRITERIA IN ORDER TO SELECT THE LOGISTIC CENTERS LOCATION." TRANSPORT 25, no. 4 (December 31, 2010): 423–32. http://dx.doi.org/10.3846/transport.2010.52.

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The main approaches which are applied to select the logistic center are the methods of gravity center, analytic hierarchy process, similarity to ideal solution, fuzzy ranking, assessment, etc. Multiple Criteria Decision‐Making (MCDM) combines analytical and inductive knowledge, describing a domain problem, which can be fuzzy and/or incomplete. The fuzzy MCDM (FMCDM) approach can explain the problem more appropriately. The purpose of the paper is to select the most suitable site for logistic centre among a set of alternatives, to help the stakeholders with the performance evaluation in an uncertain environment, where the subjectivity and vagueness of criteria are described by triangular fuzzy numbers. The paper presents a newly‐developed ARAS‐F method to solve different problems in transport, construction, economics, technology and sustainable development.

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Ye, Fei, and Qiang Lin. "Partner Selection in a Virtual Enterprise: A Group Multiattribute Decision Model with Weighted Possibilistic Mean Values." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/519629.

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This paper proposes an extended technique for order preference by similarity to ideal solution (TOPSIS) for partner selection in a virtual enterprise (VE). The imprecise and fuzzy information of the partner candidate and the risk preferences of decision makers are both considered in the group multiattribute decision-making model. The weighted possibilistic mean values are used to handle triangular fuzzy numbers in the fuzzy environment. A ranking procedure for partner candidates is developed to help decision makers with varying risk preferences select the most suitable partners. Numerical examples are presented to reflect the feasibility and efficiency of the proposed TOPSIS. Results show that the varying risk preferences of decision makers play a significant role in the partner selection process in VE under a fuzzy environment.

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Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." International Journal of Fuzzy System Applications 5, no. 4 (October 2016): 121–46. http://dx.doi.org/10.4018/ijfsa.2016100106.

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In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. The effectiveness of the proposed method is illustrated by means of a numerical example.

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Xu, Jun. "A risk attitudinal ranking approach of triangular intuitionistic fuzzy numbers and their application to MADM problems." Journal of Intelligent & Fuzzy Systems 31, no. 6 (December 5, 2016): 2919–25. http://dx.doi.org/10.3233/jifs-169175.

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Qendraj, Daniela Halidini, Evgjeni Xhafaj, Alban Xhafaj, and Etleva Halidini. "Ranking the Most Important Attributes of using Google Classroom in online teaching for Albanian Universities: A Fuzzy AHP Method with Triangular Fuzzy Numbers and Trapezoidal Fuzzy Numbers." Advances in Science, Technology and Engineering Systems Journal 6, no. 1 (January 2021): 297–308. http://dx.doi.org/10.25046/aj060134.

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Kaur, Prabjot. "Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process." Advances in Operations Research 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/987690.

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Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST), which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom called nonmembership function into the set description. In this paper, we proposed a triangular intuitionistic fuzzy number based approach for the vendor selection problem using analytical hierarchy process. The crisp data of the vendors is represented in the form of triangular intuitionistic fuzzy numbers. By applying AHP which involves decomposition, pairwise comparison, and deriving priorities for the various levels of the hierarchy, an overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our method. Lastly a sensitivity analysis is performed to find the most critical criterion on the basis of which vendor is selected.

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WAN, SHU-PING. "MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON POSSIBILITY VARIANCE COEFFICIENT OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, no. 02 (April 2013): 223–43. http://dx.doi.org/10.1142/s0218488513500128.

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Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.

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Journal articles on the topic 'Ranking triangular fuzzy numbers'

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