直觉模糊集的分解定理、表现定理和扩展原理

Decomposition theorem, representation theorem and extension principle on intuitionistic fuzzy sets

为研究模糊集截集与直觉模糊集的截集的相互关系,利用各种模糊集的截集,构造了直觉模糊集的截集,结果表明:这种方式所建立的直觉模糊集的截集概念是以往关于直觉模糊集截集概念的推广,同时这些截集也是模糊集截集概念的推广且与模糊集的截集有完全类似的性质.基于这种形式所建立的直觉模糊集的截集概念,建立了直觉模糊集的分解定理与表现定理.并进一步利用模糊集的Zadeh扩展原理,建立了直觉模糊集的扩展原理.

In order to study the relationship between the cut sets of fuzzy sets and the cut sets of intuitionistic fuzzy set, and by the use of the variety of cut sets of fuzzy sets, the cut sets of intuitionistic fuzzy set are constructed. The results show that the new proposed concept is the promotion of existing concept and having totally similar properties with fuzzy cut sets. Based on the above intuitionistic fuzzy cut sets, the decomposition theorem and representation theorem of intuitionistic fuzzy sets are established. Further, using the extension principle of Zadeh fuzzy set, the extension principle of intuitionistic fuzzy set are established.