### $\mathcal{L}$-fuzzy nonlinear approximation theory with application.

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We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect...

A new form of $\alpha $-compactness is introduced in $L$-topological spaces by $\alpha $-open $L$-sets and their inequality where $L$ is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice $L$. It can also be characterized by means of $\alpha $-closed $L$-sets and their inequality. When $L$ is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable $\alpha $-compactness and the $\alpha $-Lindelöf property...

Mostriamo che se $\left(X,d\right)$ è uno spazio metrico completo, allora è completa anche la metrica $D$, indotta in modo naturale da $d$ sul sottospazio degli insiemi sfocati («fuzzy») di $X$ dati dalle quantità approssimate. Come è ben noto, $D$ è una metrica molto interessante nella teoria dei punti fissi di applicazioni sfocate, poiché permette di ottenere risultati soddisfacenti in questo contesto.

In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities;...

In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A. George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems. 64 (1994) 395-399]. Further, a direct simple proof of the equivalences among these theorems is provided.

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.