<i>M</i>-Hazy Vector Spaces over <i>M</i>-Hazy Field

Abstract

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.

Keywords

• <i>M</i>-hazy group
• <i>M</i>-hazy ring
• <i>M</i>-hazy field
• <i>M</i>-hazy vector space
• <i>M</i>-hazy subspace
• <i>M</i>-fuzzifying convex space