双枝模糊集表现定理对偶形式

The dual form of the representation theorem of the both-branch fuzzy set

利用双枝模糊集的概念,提出了双枝模糊集表现定理的对偶形式,即交-表现定理.利用交-表现定理分析了双枝模糊集的运算性质,讨论了双枝模糊集并-表现定理与交-表现定理的关系.通过分析得到:双枝模糊集交-表现定理是单枝模糊集交-表现定理的一般形式,单枝模糊集交-表现定理是双枝模糊集交-表现定理的特例.

Based on the concept of the both-branch fuzzy set, the intersection-representation theorem of the both-branch fuzzy set is put forward. Based on intersection-representation theorems, the relationships between the intersection-representation theorem and the union-reprcsentation theorem of the both-branch fuzzy set are analyzed, and its operational property is discussed, The resuits indicate that the intersection-reprcsentation theorem of the both-branch fuzzy set is the general form of the intersection-repre- sentation theorem of the Zadeh fuzzy set, and the intersection-reprcsentation theorem of the Zadeh fuzzy set is the special form of the intersection-representation theorem of the both-branch fuzzy set.