The goal of this paper is to generalize certain results of Nguyen [1] (concerning the α-cuts of two-place functions defined by the Zadeh’s extension principle) to the case of extended two-place functions defined via a sup-tnorm convolution.

This paper presents some generalizations of the Gibbard -Satterthwaite result (1973, 1975) for fuzzy preference relations. It explores the implication of weakening the transitivity condition of the Ben Abdealziz et al.’s (2008) fuzzy manipulability concept. For this purpose, the max-min transitivity is replaced by weaker transitivity: the max-?-transitivity, where ? is a t-norm. In addition, th...

This paper deals with triangular norms and conorms defined on the extended set N of natural numbers ordered by divisibility. From the fundamental theorem of arithmetic, N can be identified with a lattice of functions from the set of primes to the complete chain {0, 1, 2, ...,+∞}, thus our knowledge about (divisible) t-norms on this chain can be applied to the study of t-norms on N. A characteri...

The transitivity of fuzzy relations with respect to a subset of quasi-linear functions in the unit interval is studied. A new construction of transitive relations with respect to an archimedean t-norm is proposed.

In this paper we consider the expansions of logics of a left-continuous tnorm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains de?ned over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the a...

We present a general formula for the intent–extent mappings of a Galois lattice generated by individual descriptions which lie in any arbitrary lattice. The formulation is unique if a natural maximality condition is required. This formulation yields, as particular cases, formal concept binary Galois lattices of Wille, those de0ned by Brito or Blyth–Janowitz, as well as fuzzy or stochastic Galoi...

The aim of this paper is to provide new results regarding the effective practical computation of t-norm-based additions of LR-fuzzy intervals.

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...

We introduce the notion of interval-valued fuzzy bi-ideals with respect to t-norm T ∗ and s-norm S∗ and investigate some of the properties. Also, the homomorphism image and inverse image are investigated. Mathematics Subject Classification: 06F35, 03G25, 03E72

We extend the M -condition from [10] and introduce the Φ -condition at zero. Next we discuss nonsquare constant in Orlicz spaces generated by an N -function Φ(u) which satisfy Φ -condition. We obtain exact value of nonsquare constant in this class of Orlicz spaces equipped with the Luxemburg norm.