Abstract
Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.
Highlights
Decision makers are often confronted with a Multiple Criteria Decision Making (MCDM) problem that finds the best option among a finite set of feasible alternatives, usually taking into account multiple conflicting criteria [1]
Among the large variety of methods developed for solving MCDM problems, Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) was initially proposed by Hwang and Yoon [1], following the rationale that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest from the negative ideal solution
In this paper we develop a mathematical programming model to determine objective weights for the interval extension of TOPSIS
Summary
Decision makers are often confronted with a Multiple Criteria Decision Making (MCDM) problem that finds the best option among a finite set of feasible alternatives, usually taking into account multiple conflicting criteria [1]. By means of TOPSIS, the ideal and anti-ideal points of the stochastic MCDM problem were determined as cumulative distribution function vectors Differing from these papers, our study derives positive and negative ideal points based upon theoretic analysis on intervals and seeks to eliminate decision bias through determining a set of objective weights associated with each criterion. Regarding the extension of TOPSIS with interval data, the weights associated with criteria are commonly determined in a subjective and arbitrary manner [6], which reveal the decision makers’ judgement or intuition based on their knowledge and preferences, but are extremely difficult to reach a consensus [19] This difficulty will be increased due to the absence of suitable decision makers but can be overcome by using an objective weights determination process [16].
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