几种新的截集及其应用

本文从“邻域”和“重域”的观点出发引入了三种新的截集：下截集，下重截集和上重截集。我们给出这些截集的性质及相应的分解定理，表现定理和扩展原理，作为应用，我们讨论了两方面的内容；一是利用落影表现理论，将一个模糊集看作“重云”的落影，然后用下生截集和落影表现理论来定义模糊集的运算，得到了与“２”一致的结果。

New Cut Sets and Their Applications

In this paper,we contribute three new cut sets such as lower cut sets,lower quasi cut set and upper quasi cut set from the point of neighborhood and quasi neighborhood and give some properties,decomposition theorem,representation theorem and extension theorem based on these cut sets.As their applications,we give new definition of operation about fuzzy sets based on the falling shadows theory and lower quasi cut sets and obtain the same results as ,we also give concept of concave fuzzy numbers and integral of fuzzy valued functions based on concave fuzzy numbers.