关系值模糊集框架中的切表示

2009 IEEE International Conference on Fuzzy Systems Pub Date : 2009-10-02 DOI:10.1109/FUZZY.2009.5277357

B. Seselja, A. Tepavčević

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引用次数: 0

摘要

广义模糊集或关系值模糊集是从集合X到关系系统S = (S, p)的映射。给出了在可切框架下用关系值模糊集表示子集集合的方法。证明了对于集合X的子集的每一个集合F，存在一个关系系统S = (S, p)和一个模糊集合μ: X→S，使得μ的切点集合重合于F。

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Representation by cuts in the framework of relational valued fuzzy sets

Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system S = (S, p). Representation of collections of subsets by relational-valued fuzzy sets in the cutworthy framework is presented. It is proved that for every collection F of subsets of a set X there is a relational system S = (S, p) and a fuzzy set μ : X → S, such that the collection of cuts of μ coincides with F.

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2009 IEEE International Conference on Fuzzy Systems

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