Optimization for multiple objectives (multi-objective optimization) has attracted signifcant attention from academia, particularly in the last 2 decades. It provides a set of optimal solutions (known as Pareto-optimal solutions). Multi-criteria decision making (MCDM) is necessary to rank and choose one of the optimal solutions for implementation. The overall purpose of this paper is to investigate extensively the sensitivity of MCDM methods including the phenomenon of rank reversal.The research evaluates the effect of three modifcations, namely, linear transformation of objectives (LTO), reciprocal objective reformulation (ROR), and removal of alternatives (RA) in the decision or objective matrix (DOM) of alternatives, on the ranking of Pareto-optimal solutions. The basic design of the study includes the use of 8 MCDM methods, 2 weighting methods (namely, entropy method and Criteria Importance Through Intercriteria Correlation, CRITIC method), and DOM datasets of 16 diverse applications from engineering. The major fndings of the study are as follows. First, certain MCDM methods such as gray relational analysis (without any weights), combinative distance-based assessment (coupled with entropy weights), and simple additive weighting (coupled with entropy or CRITIC weights) are less sensitive to the three modifcations in DOM for the applications studied. Second, the results show that weights calculated by the entropy method are more sensitive to LTO, ROR, and RA, compared to those by the CRITIC method. Third, ROR has the largest effect on ranking by MCDM methods for all of the applications studied. These fndings are useful for the application of MCDM as well as for further research.
