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.

scholarly journals A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1554
Author(s):  
Dragiša Stanujkić ◽  
Darjan Karabašević ◽  
Gabrijela Popović ◽  
Predrag S. Stanimirović ◽  
Muzafer Saračević ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Grey System Theory ◽  
Multiple Criteria ◽  
Decision Making Process ◽  
Grey System ◽  
Criteria Weights

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

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 Approach of Interval-Valued Picture Fuzzy Uncertain Linguistic Aggregation Operator and Their Application on Supplier Selection Decision-Making in Logistics Service Value Concretion

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Naeem ◽  
Muhammad Qiyas ◽  
Saleem Abdullah
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Multiple Criteria ◽  
Service Value ◽  
Logistics Service ◽  
Criteria Weights ◽  
Selection Decision ◽  
Interval Valued

With respect to multiple criteria group decision-making (MCGDM) problems in which both the criteria weights and the expert weights take the form of crisp numbers and attribute values take the form of interval-valued picture fuzzy uncertain linguistic numbers, some new group decision-making analysis methods are developed. Firstly, some operational laws, expected value, and accuracy function of interval-valued picture fuzzy uncertain linguistic numbers are introduced. Then, an interval-valued picture fuzzy uncertain linguistic averaging and geometric aggregation operators are developed. Furthermore, some desirable properties of the developed operators, such as commutativity, idempotency, and monotonicity, have been studied. Based on these operators, an approach to multiple criteria group decision-making with interval-valued picture fuzzy uncertain linguistic information has been proposed. Finally, a practical example of 3PL supplier selection in logistics service value concretion is taken to test the defined method and to expose the effectiveness of the defined model.

A New Optimization Method for Supplier Evaluation in the Context of Volume Discount

2011 ◽  
pp. 64-75
Author(s):  
Reza Farzipoor Saen
Keyword(s):  
Decision Making ◽  
Supplier Selection ◽  
Selection Process ◽  
Multiple Criteria Decision Making ◽  
Optimization Method ◽  
Multiple Criteria ◽  
Supplier Evaluation ◽  
Imprecise Data ◽  
Common Criteria ◽  
Decision Making Problem

Supplier selection is a multiple criteria decision making problem that the selection process mainly involves evaluating a number of suppliers according to a set of common criteria for selecting suppliers to meet business needs. Suppliers usually offer volume discounts to encourage the buyers to order more. To select suppliers in the presence of both volume discounts and imprecise data, this chapter proposes an optimization method. A numerical example demonstrates the application of the proposed method.

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

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.

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.

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