A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method

2021 ◽  
Vol 40 (1) ◽  
pp. 221-233
Author(s):  
Xingang Wang ◽  
Ke Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Fuzzy Theory ◽  
Research Direction ◽  
Vikor Method ◽  
Connection Number ◽  
Criterion Weight ◽  
Decision Making Problem ◽  
Electre Method ◽  
Interval Valued

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.

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

2016 ◽  
Vol 15 (05) ◽  
pp. 1157-1179 ◽  
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.

DECISION MAKING BASED ON STATISTICAL DATA, SIGNED DISTANCE AND COMPOSITIONAL RULE OF INFERENCE

2004 ◽  
Vol 12 (02) ◽  
pp. 161-190 ◽  
Author(s):  
JING-SHING YAO ◽  
MING-MIIN YU
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Statistical Data ◽  
Fuzzy Decision Making ◽  
Seamless Integration ◽  
Transit System ◽  
Signed Distance ◽  
Decision Making Problem ◽  
Interval Valued

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

scholarly journals An ELECTRE Approach for Multicriteria Interval-Valued Intuitionistic Trapezoidal Fuzzy Group Decision Making Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Sireesha Veeramachaneni ◽  
Himabindu Kandikonda
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Multiple Attribute ◽  
Electre Method ◽  
Fuzzy Group Decision Making ◽  
Magdm Problems ◽  
Interval Valued

The Multiple Criteria Decision Making (MCDM) is acknowledged as the most useful branch of decision making. It provides an effective framework for comparison based on the evaluation of multiple conflicting criteria. In this paper, a method is proposed to work out multiple attribute group decision making (MAGDM) problems with interval-valued intuitionistic trapezoidal fuzzy numbers (IVITFNs) using Elimination and Choice Translation Reality (ELECTRE) method. A new ranking function based on value and ambiguity is introduced to compare the IVITFNs, which overcomes the limitations of existing methods. An illustrative numerical example is solved to verify the efficiency of the proposed method to select the better alternative.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

scholarly journals AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS

2015 ◽  
Vol 22 (1) ◽  
pp. 122-141 ◽  
Author(s):  
Dragisa STANUJKIC
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
System Approach ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Performance Ratings ◽  
Triangular Fuzzy Numbers ◽  
Moora Method ◽  
Interval Valued

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.

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