直觉模糊集新截集与直觉模糊向量子空间

A new cut set of intuitionistic fuzzy sets and intuitionistic fuzzy vector subspace

为给出直觉模糊向量空间的一种合理架构并建立与经典向量空间理论的联系,给出了直觉模糊集的一种新的截集,利用新的截集给出了直觉模糊向量子空间的定义.讨论了所建立的直觉模糊向量子空间的性质,研究了直觉模糊仿射集与直觉模糊子空间的关系.结果表明:由于该截集实际上推广了原有的直觉模糊集的截集,所以依据该截集建立的直觉模糊向量子空间理论推广了原有的一些直觉模糊向量子空间的理论.研究结果推广了现有直觉模糊向量子空间的一些结果,该研究方法也可以应用到凸直觉模糊集等方面的研究中.

In order to give a reasonable framework for intuitionistic fuzzy vector space and establish a relationship with the classical vector space theory, a new cut set of intuitionistic fuzzy sets is introduced by using new cuts of sets, which gives the definition of intuitionistic fuzzy vector subspace. The properties of Intuitionistic fuzzy vector subspace established is discussed, the relationship between intuitionistic fuzzy affine sets and intuitionistic fuzzy subspace is studied. Actually, due to the new cut sets which create to develop the original intuition cut set of fuzzy sets and the intuitionistic fuzzy vector subspace dependent on the new cut sets also improve the original one. The results generalize the ones of intuitionistic fuzzy vector subspace studies at present, so the method can be applied in the studies of convex intuitionistic fuzzy sets.