Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded...Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded closed sets (nonfuzzy) in X. If A, B∈(?)(X) and ω_α(A), ω_α(B)∈ CB(X), we can define ρ_α(A, B) = inf{d(x,y):x∈ω_α(A),y∈ω_α(B) } , D_α(A,B)= H(ω_α(A),ω_α(B)),where H is Hausdorff distance induced by d. Definition. Let F be a fuzzy mapping over X, i.e. a mapping from X to (?)(X). Write F (x) =F_x. To the point x_*∈X, if F_x_*(x_*)= α, then we say that the fixed degree of x_*展开更多
文摘Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded closed sets (nonfuzzy) in X. If A, B∈(?)(X) and ω_α(A), ω_α(B)∈ CB(X), we can define ρ_α(A, B) = inf{d(x,y):x∈ω_α(A),y∈ω_α(B) } , D_α(A,B)= H(ω_α(A),ω_α(B)),where H is Hausdorff distance induced by d. Definition. Let F be a fuzzy mapping over X, i.e. a mapping from X to (?)(X). Write F (x) =F_x. To the point x_*∈X, if F_x_*(x_*)= α, then we say that the fixed degree of x_*
