M-Hazy Module and Its Homomorphism Theorem

Based on a completely distributive lattice M , we propose a new fuzzification approach to a module, which leads to the concept of an M -hazy module. Different from the traditional fuzzification approach that defines a fuzzy algebra as a fuzzy subset of a classical algebra, we introduce an M -hazy module by fuzzifications of algebraic operations. Then, we investigate the fundamental properties of M -hazy modules and M -hazy submodules. In particular, we present the M -hazy module homomorphism theorem.