Solution of Fuzzy Relation Equations Using the Rule of Exclusion

Abstract

This paper proposes an efficient way of solving Sup ・ min composite relation equations. The proposed method can lead all independent solutions which do not include each other. The independent solutions are obtained by simple logical operations, utilizing both the criterion matrix and the auxiliary matrix. These matrices are derived from the relationship between fuzzy relation R and fuzzy set b. Furthermore, applying the rule of exclusion, it is possible to remove some awkward elements which result in redundant solution sets.