Properties of Composition of Fuzzy Relations and its Verifications

This paper, deals with fundamental notions in pure and applied sciences, i.e., basic operations related to fuzzy relations. The composition of fuzzy relations are defined in two ways such as max-min composition and max-product composition with suitable example. This paper also introduces the properties of composition of fuzzy relations. The newly introduced properties inculcates zero, identity, equal, not-equal, subset, associative, union, intersection and distributive fuzzy relations. Finally, the paper verifies the properties of composition of fuzzy relations using some numerical values for 2x2 order of matrix. Also gives some exercise problems related to the above concepts with accurate answer keys.