Regular and strongly regular relations induced by fuzzy subhypermodules

Binary equivalence relations have been investigated in hyperstructures and specially hypermodules theory. By regular and strongly regular relation, we can construct a hypermodule structure on the quotient set. The motivation for such an investigation is to generalize the concept of quotient hypermodule constructed by fuzzy subhypermodules and isomorphism theorems. Also, we consider that when the fuzzy subhypermodule is normal, the equivalence relation defined by J. Zhan et al. on hypermodules is strongly regular. Moreover, the hyperadditions defined by J. Zhan et al. on quotient hypermodules are just additions. Also, by the concept of quotient hypermodules, we present an exact sequence of hypermodules and construct an exact sequence of hypermodules by fuzzy subhypermodules. Also, we define a chain complex and a homology of chain complex.