TOPSIS FOR MODM

In this study, we extend TOPSIS to solve a multiple objective decision making problem. The principle of compromise (of TOPSIS) for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution. Thus, we reduce a k-dimensional objective space to a two-dimensional objective space by a first-order compromise procedure. We then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria. We obtain a single-objective programming problem by using the max-min operator for the second-order compromise operation. To illustrate the procedure, the Bow River Valley water quality management problem is solved by use of TOPSIS.