Characterization of aggregate fuzzy membership functions using Saaty's eigenvalue approach

This paper describes and extends Saaty's eigenvalue approach to fuzzy membership determination. A genetic algorithm-based procedure is adopted to minimize the failure rates in fuzzy membership determination using Saaty's eigenvalue approach. The proposed method is then extended to develop an aggregate fuzzy membership function using multiple decision-maker environment. A theoretical framework for understanding the magnitude of failures with the increase in the cardinality of fuzzy sets is provided. Several researchers have shown that characterizing fuzzy memberships functions using the AHP lead to certain failures. We illustrate how a genetic algorithm-based procedure can be used to lower such failures.