The category FGrp of fuzzy groups is not equivalent to the category Grp of classical groups

Abstract

In this paper, the concept of strong homomorphism of fuzzy group in the sense of [ 4 ] is given. The fundamental homomorphism theorem of fuzzy group, in the sense of strong homomorphism, is also obtained. We built a category FGrp of fuzzy groups and strong homomorphism and show that category FGrp and the category Grp of group and homomorphism are not equivalent. These discussions show that fuzzy group is different from classical group.