基于各种截集的直觉模糊向量子空间

Intuitionistic Fuzzy Vector Subspaces based on Different Cut Sets

首先,利用模糊集的上截集、下截集、上重截集和下重截集的各种"凸组合",给出直觉模糊集的下截集、上重截集和下重截集的定义,并研究了其性质。其次,将模糊集的上截集、下截集、上重截集和下重截集作为经典向量子空间定义了相应的直觉模糊向量子空间,研究了各个直觉模糊子空间的性质。最后,讨论了各种直觉模糊向量子空间的关系。由于这些截集的建立实质上是已有直觉模糊集截集的推广,所以研究的结果丰富了已有的直觉模糊向量空间理论。

Firstly, using the various convex combination of the upper cut, lower cut, upper-Q cut and lower-Q cut of fuzzy set, the corresponding cuts of intuitionistic fuzzy set were defined, and their properties were studied. Secondly, intuitionistic fuzzy vector subspace was defined based on the corresponding cuts of fuzzy sets, properties of the intuitionistic fuzzy subspace were discussed. Finally, the relationships between all kinds of intuitionistic fuzzy subspace were explored. Because these cut sets were extended the existing cut sets on intuitionistic fuzzy sets, the results enriched the existing intuitionistic fuzzy vector space theory.