Abstract

A fuzzy ordering for fuzzy sets on R n is presented by a fuzzy relation on R n× R n which is induced by closed convex cones. The suitability of the fuzzy order is discussed using the axioms A 1–A 7 in (Fuzzy Sets and Systems 118 (2001) 375). For fuzzy sets on R n which are incomparable with respect to the fuzzy order, a method to evaluate the degree of satisfaction regarding the fuzzy order is presented by using a subsethood degree. Approximation by discrete cases is discussed for numerical calculation on the degree of the fuzzy order. Numerical examples are also given to illustrate our idea.

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