Ordering of convex fuzzy sets - A brief survey and new results

Abstract

Concerning with the topics of a fuzzy max order, a brief survey on ordering of fuzzy numbers is presented in this article, and we will consider an extension to that of fuzzy sets. An extension of the fuzzy max order as a pseudo order is investigated and defined on a class of fuzzy sets on ℝn (n ≥ 1). This order is developed by using a non-empty closed convex cone and characterized by the projection into its dual cone. Especially a structure of the lattice can be illustrated with the class of rectangle-type fuzzy sets.