Post factum analysis in TOPSIS based decision making method. (30th December 2019) - Dutta, Bapi; Singha, Tanima; Goh, Mark; Lamata, Maria-Teresa; Verdegay, Jose-Luis
Highlights: Propose a post factum analysis framework for TOPSIS based decision making. Analyze the dynamics of decision information change over recommendations. Develop algorithms to explore different achievable targets set by decision maker. Demonstrate the effectiveness of the proposal as a tool of robust decision analysis. Abstract: 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.