Definition 1.1 (see [1]). A triple (X ,M,∗), where X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set on X2× (0,∞), is said to be a fuzzy metric space (in the sense of George and Veeramani) if the following conditions are satisfied for all x, y ∈ X and s, t > 0: (GV-1) M(x, y, t) > 0; (GV-2) M(x, y, t)= 1 if and only if x = y; (GV-3) M(x, y, t)=M(y,x, t); (GV-4) M(x, y,·) is c...

In this paper, first we give the definitions of various indicators of fuzzy relations and their basic properties. Then we investigate the relationships between these indicators, particularly between those of T-transitivity, negative S-transitivity, T–S-semitransitivity and T–S-Ferrers property. The investigation is divided into three parts: results in the general case, results under a condition...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...

T-norm based fuzzy logics are usually considered as truth preserving, that is, taking 1 as the only truth value to be preserved in inferences. In this paper we study t-norm based fuzzy logics preserving degrees of truth, that is, preserving the lower bounds of the truth degrees of the premises. These logics are axiomatizable by using a restricted form of Modus Ponens together with the rule of A...

This paper is a humble homage to Enric Trillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of these models, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics. We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence o...

This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ∆-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate ...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages ...