Paramentric orders on fuzzy numbers and their roles in fuzzy optimization problems

Two types of parametric order relations on the class of symmetric fuzzy numbers generated by shape functions are defined. The first one is same as the one defined by the present author in [3]. The notion of a “mutually nondominant” set of fuzzy numbers is introduced. A minimal solution means a solution nondominated with respect to minimizing under the fuzzy max order. A necessary and sufficient condition for a set of mutually non-dominant minimal solutions to be exhaustively detected by the order criterion of the first type is given. A necessary and sufficient condition for the same purpose as above is given for the second type one. As an application of the parametric orders, a numerical example of fuzzy shortest route problem is illustrated.