Optimization with linguistic variables

Abstract

We consider fuzzy mathematical programming problems (FMP) in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base is supposed to consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variables, and the consequence part is either a linguistic value of the objective function or a linear combination of the crisp values of the decision variables. In this paper we suggest the use of an adequate fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and to solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem. Furthermore, we illustrate how the optimal solution may change if we are able to refine the rule base by introducing some non-monotonicity (dependency) rules.