The dual form of representation theorem of single-branch fuzzy set
Jiqin Liu · Journal of Shandong University · 2006
Using the product formula of number and nest of sets: λ(H(λ)(u)=)λ∨H(λ),the dual form of representation theorem of fuzzy set that is intersection-representation theorem is given.It is obtained that ∩λ∈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 discussed.