Post factum analysis in TOPSIS based decision making method

TOPSIS (Technique of Order Preference by Similarity to Ideal Solution) is a popular decision-making technique used to rank a discrete set of alternatives based on the premise that a good alternative should simultaneously have the shortest distance from a positive ideal solution and the farthest distance from a negative ideal solution. Sometimes, ambiguity or impreciseness in the decision information may lead a decision maker to raise questions about the robustness of the recommendation of a TOPSIS based decision-making model. To address the concerns of the decision maker, this paper therefore proposes a sensitivity and stability analysis framework to address the robustness of the recommendations and the different achievable targets set by the decision maker. Specifically, we analyze the effect of a change in the rating of an alternative under a criterion and determine the appropriate conditions to predict how the closeness coefficients change. Through this analysis, we investigate the minimal performance change that is required in an alternative's rating under a criterion to achieve a particular target set by decision maker when the rest of the decision information set remains unaltered. An algorithm is provided to find the set of criteria whereby changing a criterion of a alternative, it can obtain another alternative's rank. We investigate the behaviour of the closeness coefficient of an alternative when a criterion rating changes, and provide two algorithms to identify the upper and lower-rank achievable alternatives. Subsequently, we describe the rank reversal of a pair of alternatives and introduce the concept of a rank sensitive interval. A numerical example on university ranking is provided to demonstrate the validity of the proposed model. (C) 2019 Elsevier Ltd. All rights reserved.