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.