Reasonable properties for the ordering of fuzzy quantities (II)
As a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fufilment of reasonable properties in the third class of ordering approaches. To do so we briefly introduce fuzzy relations on which the third class of approaches is based. Then we recall some transitivity-related concepts and an ordering procedure based on a acyclic fuzzy relation. Acyclicity is a very weak restriction on a fuzzy relation. We prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity. So we give a widely applicable formulation to derive a total ranking order from a fuzzy relation. With our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part I. (C) 2001 Elsevier Science B.V. All rights reserved.
fuzzy relation acyclicity transitivity ranking of fuzzy quantities