Weighted Constraints in Fuzzy Optimization

Abstract

Many practical optimization problems are characterized by someflexibility in the problem constraints, where this flexibility canbe exploited for additional trade-off between improving theobjective function and satisfying the constraints. Especially indecision making, this type of flexibility could lead to workablesolutions, where the goals and the constraints specified bydifferent parties involved in the decision making are traded offagainst one another and satisfied to various degrees. Fuzzy setshave proven to be a suitable representation for modeling this typeof soft constraints. Conventionally, the fuzzy optimizationproblem in such a setting is defined as the simultaneoussatisfaction of the constraints and the goals. No additionaldistinction is assumed to exist amongst the constraints and thegoals. This report proposes an extension of this model forsatisfying the problem constraints and the goals, where preferencefor different constraints and goals can be specified by thedecision-maker. The difference in the preference for theconstraints is represented by a set of associated weight factors,which influence the nature of trade-off between improving theoptimization objectives and satisfying various constraints.Simultaneous weighted satisfaction of various criteria is modeledby using the recently proposed weighted extensions of(Archimedean) fuzzy t-norms. The weighted satisfaction of theproblem constraints and goals are demonstrated by using a simplefuzzy linear programming problem. The framework, however, is moregeneral, and it can also be applied to fuzzy mathematicalprogramming problems and multi-objective fuzzy optimization.wiskundige programmering;fuzzy sets;optimalisatie