An Interval-Valued Pythagorean Fuzzy Outranking Method with a Closeness-Based Assignment Model for Multiple Criteria Decision Making

The method of ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) is a well-known and widely used outranking method for handling decision-making problems. The purpose of this paper is to develop an interval-valued intuitionistic fuzzy ELECTRE (IVIF-ELECTRE) method and apply it to multiple criteria decision analysis (MCDA) involving the multiple criteria evaluation/selection of alternatives. Using interval-valued intuitionistic fuzzy (IVIF) sets with an inclusion comparison approach, concordance and discordance sets are identified for each pair of alternatives. Next, concordance and discordance indices are determined using an aggregate importance weight score function and a generalised distance measurement between weighted evaluative ratings, respectively. Based on the concordance and discordance dominance matrices, two IVIF-ELECTRE ranking procedures are developed for the partial and complete ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a multiple criteria decision-making problem of watershed site selection. A comparative analysis of other MCDA methods is conducted to demonstrate the advantages of the proposed IVIF-ELECTRE methods. Finally, an empirical study of job choices is implemented to validate the effectiveness of the current methods in the real world.

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Comparative analysis of evolutionary algorithms for multiple criteria decision making with interval-valued belief distributions

Intelligent Decision Technologies ◽

10.3233/idt-190125 ◽

2020 ◽

Vol 14 (3) ◽

pp. 373-391

Author(s):

Guangyan Lu ◽

Wenjun Chang

Keyword(s):

Decision Making ◽

Particle Swarm Optimization ◽

Comparative Analysis ◽

Evolutionary Algorithms ◽

Optimization Algorithm ◽

Particle Swarm Optimization Algorithm ◽

Multiple Criteria Decision Making ◽

Multiple Criteria ◽

Swarm Optimization ◽

Interval Valued

In multiple criteria decision making (MCDM) with interval-valued belief distributions (IVBDs), individual IVBDs on multiple criteria are combined explicitly or implicitly to generate the expected utilities of alternatives, which can be used to make decisions with the aid of decision rules. To analyze an MCDM problem with a large number of criteria and grades used to profile IVBDs, effective algorithms are required to find the solutions to the optimization models within a large feasible region. An important issue is to identify an algorithm suitable for finding accurate solutions within a limited or acceptable time. To address this issue, four representative evolutionary algorithms, including genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and gravitational search algorithm, are selected to combine individual IVBDs of alternatives and generate the minimum and maximum expected utilities of alternatives. By performing experiments with different numbers of criteria and grades, a comparative analysis of the four algorithms is provided with the aid of two indicators: accuracy and efficiency. Experimental results indicate that particle swarm optimization algorithm is the best among the four algorithms for combining individual IVBDs and generating the minimum and maximum expected utilities of alternatives.

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Multiple criteria decision making method based on normal interval-valued intuitionistic fuzzy generalized aggregation operator

Complexity ◽

10.1002/cplx.21654 ◽

2015 ◽

Vol 21 (5) ◽

pp. 277-290 ◽

Cited By ~ 27

Author(s):

Peide Liu ◽

Fei Teng

Keyword(s):

Decision Making ◽

Multiple Criteria Decision Making ◽

Aggregation Operator ◽

Multiple Criteria ◽

Intuitionistic Fuzzy ◽

Interval Valued

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Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Discrete Dynamics in Nature and Society ◽

10.1155/2019/1527612 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

M. Sarwar Sindhu ◽

Tabasam Rashid ◽

Agha Kashif ◽

Juan Luis García Guirao

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Real Life ◽

Multiple Criteria Decision Making ◽

Multiple Criteria ◽

Decision Makers ◽

Occurrence Probability ◽

Hesitant Fuzzy Sets ◽

Life Problems ◽

Interval Valued

Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

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A prioritized aggregation operator-based approach to multiple criteria decision making using interval-valued intuitionistic fuzzy sets: A comparative perspective

Information Sciences ◽

10.1016/j.ins.2014.05.018 ◽

2014 ◽

Vol 281 ◽

pp. 97-112 ◽

Cited By ~ 46

Author(s):

Ting-Yu Chen

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Multiple Criteria Decision Making ◽

Intuitionistic Fuzzy Sets ◽

Aggregation Operator ◽

Multiple Criteria ◽

Comparative Perspective ◽

Intuitionistic Fuzzy ◽

Prioritized Aggregation Operator ◽

Interval Valued

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New Method for Solving a General Multiple Criteria Decision-Making Problem Under Risk in Fuzzy Environment

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622016500279 ◽

2016 ◽

Vol 15 (05) ◽

pp. 1157-1179 ◽

Cited By ~ 3

Author(s):

N. Thillaigovindan ◽

S. Anita Shanthi ◽

J. Vadivel Naidu

Keyword(s):

Decision Making ◽

Multiple Criteria Decision Making ◽

Multiple Criteria ◽

Fuzzy Soft Set ◽

Score Functions ◽

Fuzzy Environment ◽

Criterion Weight ◽

Decision Making Problem ◽

Criteria Weights ◽

Interval Valued

This paper considers a multiple criteria decision-making (MCDM) problem under risk in fuzzy environment in its general form. There are m alternatives which need to be ranked on the basis of a set of n criteria. The alternatives and the criteria are evaluated based on a set of l characteristics. The entire data is presented in the form of interval valued intuitionistic fuzzy soft set of root type. In addition each criterion is assigned a subjective criterion weight based on expert’s evaluation and each characteristic is assigned a probability weight on the basis of decision maker’s knowlege and understanding of the importance of the characteristic. This problem may be called as a MCDM problem under risk in fuzzy environment in its general form. A method for ranking the alternatives using the new score functions, prospect theory and method of determining the optimum criteria weights is explained. An algorithm is developed for this purpose and its working illustrated with a suitable example.

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