In fuzzy logic in wider sense t norms got a prominent r ole in recent times In many valued logic the Lukasiewicz systems the G odel sytems and also the product logic are t norm based The present paper discusses the more general problem of the adequate axiomatizability for such t norm based logical systems in general survey ing results of the last years

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...

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...

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 ...

CADIAG-2 is a successful expert system assisting in the differential diagnosis in internal medicine. With its aid, conjectures about present diseases are derived from possibly vague information about a patient’s symptoms. In this paper we provide a mathematical formalisation of the inferential mechanism of CADIAG-2. A Gentzen-style calculus for the resulting logic is introduced and used to comp...