Fuzzy quasi-triangular spaces, fuzzy sets of Pompeiu-Hausdorff type, and another extensions of Banach and Nadler theorems

摘要

Let A $mathcal{A}$ be an index set, and C = { C α } α ∈ A ∈ [ 1 ; ∞ ) A $C={C_{lpha}}_{lphain mathcal{A}}in{}[1;infty)^{mathcal{A}}$ . Fuzzy quasi-triangular space is defined to be ( X , M C ; A , ∗ ) $(X,mathcal{M}_{C;mathcal{A}},st)$ , where X is a nonempty set, a fuzzy family M C ; A = { M α : X × X × ( 0 ; ∞ ) → ( 0 ; 1 ] , α ∈ A } $mathcal{M}_{C;mathcal{A}}={M_{lpha }:Ximes Ximes(0;infty)ightarrow(0;1],lphainmathcal{A}}$ satisfies ∀ α ∈ A ∀ x , y , z ∈ X ∀ t , s ∈ ( 0 ; ∞