M-Hazy Module and Its Homomorphism Theorem

Abstract

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.