In this paper two methods are proposed to measure the l-T-inconditionality character of any fuzzy relation for any continuous t-norm T, and it is studied when both methods result to be equivalent.

Special implications were introduced by Hájek and Kohout [Fuzzy implications and generalized quantifiers, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 4 (1996) 225–233] in their investigations on some statistics on marginals. They have either suggested or only partially answered three important questions, especially related to special implications and residuals of t-norms. In this work we in...

The main concern of this paper is to introduce and characterize the class of operators on a finite chain L, having the same properties of pseudo-smooth uninorms but without commutativity. Moreover, in this case it will only be required the existence of a one-side neutral element. These operators are characterized as combinations of A N D and O R operators of directed algebras (smooth t-norms an...

In this paper, we observe and compare results concerning solvability of systems of fuzzy relation equations with different types of composition. In fact, two types of composition are considered sup−∗ and inf → composition where ∗ is a continuous tnorm and→ is residuation operation with respect to the t-norm ∗.

This paper deals with a kind of implications defined from t-norms, t-conorms and strong negations on a finite chain, through the expression I(x,y) = S(N(x),T (x,y)), and called QL-implications. We mainly study those QL-implications derived from smooth t-norms and t-conorms. It is characterized when functions defined in this way are implication functions, and their analytical expression is given...

Recommended by Akbar Rhemtulla We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

Keywords: Fuzzy variable Independence Operation t-norm Convergence Law of large numbers a b s t r a c t T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variable...

This paper deals with Lipschitz triangular norms (t-norms). A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitz property for arbitrary t-norms is introduced. Some remarkable examples of non-Lipschitz continuous ones are provided.

In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is proved that if t-norm is chosen other than ”min” then decomposition theorem of a fuzzy norm into a family of crisp norms may not hold. We study some basic results on finite dimensional fuzzy normed linear spaces in general t-norm setting. 2010 AMS...

In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess t...