双枝模糊集(Ⅲ)

BOTH BRANCH FUZZY SETS(Ⅲ) *

提出双枝模糊集Ｓ的理论，本课题是［Ⅰ，Ⅱ］研究的继续．在单枝模糊集理论（Ｌ．Ａ．ＺａｄｅｈＦｕｚｚｙＳｅｔＴｈｅｏｒｙ）研究中，由于引进λ－截集Ｓλ的概念，便产生了单枝模糊集的并－普通分解定理［３］，交－普通分解定理［４］．［Ⅰ，Ⅱ］提出了双枝模糊集Ｓ，由于引进了λ－截集Ｓλ的概念，便产生了双枝模糊集Ｓ的并－普通分解定理，交－普通分解定理．人们自然提出这样的问题：双枝模糊集可以分解成若干个普通集Ｓλ；双枝模糊集Ｓ是否能分解成若干个模糊集Ｓα？本文的研究说明：双枝模糊集Ｓ可以分解成若干个模糊集Ｓα．（一个单枝模糊集Ａ也可以分解成若干个模糊集Ａα，但是在单枝模糊集理论中没有被人们去研究．）本文给出Ｓ的α－嵌入集Ｓα的概念，提出Ｓ的α－嵌入定理，Ｓ的α－嵌入模糊分解定理．

Proposes the theory of both branch fuzzy set which is the continuation of the theme(Ⅰ,Ⅱ). In the study of one branch fuzzy set theory(L. A. Zadeh fuzzy set theory),due to the introduction of λ cutset S λ ,there generate union ordinary resolution theorem,intersection ordinary resolution theorem of one branch fuzzy set. The theme(Ⅰ,Ⅱ) proposed both branch fuzzy set S . Due to the introduction of λ cutset S λ ,there generate union ordinary resolution theorem,intersection ordinary resolution theorem of boht branch fuzzy set S . Naturally people propose such questions: both branch fuzzy set can be resolved into many ordinary sets S λ ;can both branch fuzzy set S be resolved into many fuzzy sets S α . (One branch fuzzy set A can also be resolved into many fuzzy sets A α ,which has not been studied in one branch fuzzy set theory). This paper proposes the concept of α imbedding set S α of S , α imbedding theorem of S , α imbedding fuzzy resolution theorem of S .