A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones
A fuzzy ordering for fuzzy sets on R-n is presented by a fuzzy relation on R-n x 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. (C) 2002 Elsevier Science B.V. All rights reserved.
multi-dimensional fuzzy set convex cone fuzzy relation fuzzy partial ordering degree of order multi-criteria decision making