摘要
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。我们给出了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，然后用下重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；二是利用下截集给出凹模糊数的定义。
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.
出处
《模糊系统与数学》
CSCD
1997年第1期37-43,共7页
Fuzzy Systems and Mathematics
关键词
模糊集
截集
集合套
随机集
凹模糊数
下截集
Fuzzy Sets
Cut Sets
Nested Sets
Random Sets
Concave fuzzy number
Integrals
