格区间值模糊集的分解定理和表现定理(Ⅰ)

Decomposition theorem and representation theorem of the interval value fuzzy set

针对区间值模糊集合,在完备格的基础上建立一种更为广泛的区间值模糊集——格区间值模糊集,构造了8种新的格区间值模糊集截集和相应的一种新的格区间与格区间值模糊集截集的运算,进而根据已有的模糊集合的分解定理和表现定理,给出了格区间值模糊集的两条分解定理和两条表现定理.

The lattice interval fuzzy set, a kind of more widespread interval fuzzy set, is established based on the complete lattice. Eight new sorts of the cut sets of lattice interval fuzzy set are given, and a new operation between the lattice interval fuzzy sets is constructed. Then according to the existing decomposition theorem and representation theorem of the fuzzy set, two decomposition theorems and two representation theorems of the lattice interval fuzzy set are given.