General Method to Generate Fuzzy Equivalence Relations in Matrix Form

Abstract

In this paper, new method to generate fuzzy equivalence relations in matrix form is considered, it is not easy to check fuzzy relation in matrix form if it is equivalence relation or not, and if it is transitive or not transitive. We start building fuzzy equivalence relation in matrix forms 3 × 3 and 4 × 4 matrices, then by using mathematical induction we will build general method that generates fuzzy equivalence relations of the form n × n matrices.

Key words and phrases. Fuzzy Sets, Operations on Fuzzy Sets, Fuzzy Relations, Fuzzy Equivalence Relations.