Fuzzy sets and quotient spaces

Abstract

This paper discussed the relation between FS and QS by theory of the isomorphism and homomorphism of fuzzy sets, and two main conclusions are reached. Firstly, for any group of fuzzy sets which are isomorphic, a quotient space could be defined uniquely, and a quotient structure space is determined. Secondly, for any group of fuzzy relations which are isomorphic, similarly a fuzzy quotient space could be defined uniquely, and a fuzzy quotient structure space is determined. Moreover, the construction of fuzzy quotient space is given. Finally, we discussed their related properties.