In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

We develope a construction of an L-fuzzy valued measure by extending a measure defined on a σ-algebra of crisp sets to an L-fuzzy valued TM-countably additive measure defined on a TMclan of L-fuzzy sets in the case when operations for L-fuzzy sets and L-fuzzy real numbers are based on the minimum t-norm TM. Keywords— L-fuzzy set, L-fuzzy real number, L-fuzzy valued measure.

Inspired by an open problem of Alsina, Frank and Schweizer, k-Lipschitz t-norms are studied. The k-convexity of continuous monotone functions is introduced. Additive generators of k-Lipschitz tnorms are completely characterized by means of k-convexity. For a given k ∈ [1,∞[ the pointwise infimum A∗k of the class of all k-Lipschitz t-norms is introduced.

We define the fuzzy description logic ALCHNM based on the t-norm of Nilpotent Minimum and we prove its reduction to the crisp description logic ALCH. Hence we prove decidability results for ALCHNM.

Article history: Received 29 September 2011 Received in revised form 31 October 2012 Accepted 21 November 2012 Available online 13 December 2012

This paper studies a renewal reward process with fuzzy random interarrival times and rewards under the >-independence associated with any continuous Archimedean t-norm >. The interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are >-independent fuzzy variables. Under these conditions, some limit theorems in mean...

In this paper we consider algebras of fuzzy truth values equipped with an implication operation. Generalizing the definition of type-1 fuzzy implications, we discuss extended fuzzy S-implications and coimplications and also extended residual implications and coimplications, in particular to the extended residual of minimum. We study the algebraic properties of these operations and their relatio...

We obtain estimates in Besov, Triebel–Lizorkin and Lorentz spaces of differential forms on Rn in terms of their L1 norm.

The representation theorem Cor F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F -transitive fuzzy relations on a set X, F being an Archimedean t-norm, is dense in the set of Ztransitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.