On an equivalence of fuzzy subgroups. III (Q1415082)

Summary: This paper is the third in a series of papers studying equivalence classes of fuzzy subgroups of a given group under a suitable equivalence relation [for part II see Fuzzy Sets Syst. 136, No. 1, 93-104 (2003; Zbl 1019.20033)]. We introduce the notion of a pinned flag in order to study the operations sum, intersection and union, and their behavior with respect to the equivalence. Further, we investigate the extent to which a homomorphism preserves the equivalence. Whenever the equivalences are not preserved, we have provided suitable counterexamples.