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.

中文翻译：

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M朦胧场上的M朦胧向量空间

从经典代数到模糊二元运算的泛化是模糊代数领域的重要发展。本文提出了向量空间的领域上一个新的概括，这就是所谓中号在-hazy向量空间中号-hazy场。研究了M朦胧场，M朦胧向量空间和M朦胧子空间的一些基本性质，并证明了一些重要的结果。此外，研究了M-朦胧向量空间的线性变换，并证明了它们的重要结果。最后表明，M-模糊凸空间是由M-朦胧子空间引起的。M朦胧的向量空间。