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.
Keywords :
fuzzy set theory; fuzzy quotient structure space; fuzzy set theory; homomorphism theory; isomorphism theory; Application software; Cognition; Computer science; Data mining; Fuzzy set theory; Fuzzy sets; Gold; Humans; Set theory; Topology; fuzzy equivalent relation; fuzzy set theory; granule computing; quotient space theory;
