M-Hazy Vector Spaces over M-Hazy Field

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

Automated summary

This paper discusses M-hazy vector spaces and related concepts, studies some fundamental properties and derives important results, ultimately proving that M-fuzzifying convex spaces are induced by a subspace of M-hazy vector space.