MTL-algebras are algebraic structures for the Esteva-Godo monoidal tnorm based logic (MTL), a many-valued propositional calculus that formalizes the structure of the real interval [0, 1], induced by a left-continuous t-norm. Given a complete MTL-algebra X , we define the weak forcing value |φ|X and the forcing value [φ]X , for any formula φ of MTL in X . We establish some arithmetical propertie...

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...

We study the transitivity of fuzzy preference relations, often considered as a fundamental property providing coherence to a decision process. We consider the transitivity of fuzzy relations w.r.t. conjunctors, a general class of binary operations on the unit interval encompassing the class of triangular norms usually considered for this purpose. Having fixed the transitivity of a large prefere...

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.