单枝模糊集表现定理对偶形式

The dual form of representation theorem of single-branch fuzzy set

利用数与集合套的数积:λH(λ)(u)=λ∨H(λ)这种定义形式,给出了单枝模糊集表现定理的对偶形式,即交-表现定理.从而得出,对于任一集合套H(λ),∩λ∈[0,1]λH(λ)也表示一个模糊集.分析了模糊集交-表现定理与并-表现定理的关系,并在交-表现定理基础上进一步讨论了模糊集的一些运算性质.

Using tlie product formula of number and nest of sets： λ×H（λ）（u）=λVH（λ）, the dual form of representation theorem of fuzzy set that is intersection- representation theorem is given. It is obtained that ∩λ∈[0.1]λ×H（λ） is also a fuzzy set for any nest of sets H（λ）. On the basis of the intersection- representation theorems, the relationship between intersection- representation theorem and union- representation theorem are analyzed, and some operational properties are further diseussed.