Abstract
The VIKOR method was developed for multicriteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the given weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. Here, the VIKOR method is used for two timestandt+1. In order to calculate the progress or regression via Malmquist productivity index, the positive and negative ideals at timestandt+1are calculated first. Then we introduce the multi-criteria ranking index based on the particular measure of “closeness” to the ideal solution and calculate the separation of each alternative from the ideal solution at timestandt+1. Then we use the Malmquist productivity index to calculate the progress or regression of all alternatives. In this paper, productivity of alternatives available in decision matrix with interval numbers and their improvement or deterioration is researched. To achieve this practical goal, use of extended VIKOR is made to calculate Malmquist productivity index for multicriteria decision-making (MCDM) problem with interval numbers, and by applying Malmquist productivity index, productivity rate of growth for alternatives is calculated. Finally, a numerical example illustrates and clarifies the main results developed in this paper.
Highlights
Multi criteria optimization is the process of determining the best feasible solution according to the established criteria
We introduce the multi-criteria ranking index based on the particular measure of “closeness” to the ideal solution and calculate the separation of each alternative from the ideal solution at times t and t + 1
A multiattribute decision-making (MADM) problem can be defined as shown in Table 1 where A1, A2, . . . , Am are possible alternatives among which decision makers have to choose, C1, C2, . . . , Cn are criteria with which alternative performance is measured, fij is the rating of alternative Ai with respect to criterion Cj, and wj is the weight of criterion Cj [3,4,5]
Summary
Multi criteria optimization is the process of determining the best feasible solution according to the established criteria. We extend the concept of VIKOR method to develop a methodology for the calculation of progress or regression via Malmquist productivity index for MADM problems with interval numbers. As it was said in the introduction, the interval numbers are more suitable to deal with the decision-making problems in the imprecise and uncertain environment, because they are the simplest form of representing uncertainty in the decision matrix. We introduce a new algorithm for the calculation of progress or regression via extended VIKOR and Malmquist productivity index for MADM problem with interval numbers.
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