T -product extensions (where T is a continuous t-norm) of a system of low-dimensional possibility distributions form an important class of solutions of the so-called possibilistic marginal problem. Nevertheless, they can differ from each other, e.g., from the viewpoint of inference. Therefore the need for their interpretation is obvious. To find it, we identify any possibility distribution with...

In this paper a variation of the fibred semantics of D. Gabbay called plain fibring is proposed, with the aim of combining logics given by matrix semantics. It is proved that the plain fibring of matrix logics is also a matrix logic. Moreover, it is proved that any logic obtained by plain fibring is a conservative extension of the original logics. It is also proposed a simpler version of plain ...

The class of discrete uninorms U such that their underlying t-norm T and t-conorm S are smooth is studied. The different cases combining when T is the minimum or the Łukasiewicz t-norm and S is the maximum or the Łukasiewicz t-conorm, are characterized and the number of discrete uninorms with these underlying operators is given. It is also studied the general case when T and/or S are smooth, bu...

1.1. t-norms. A triangular norm (shortly t-norm) is a binary operationT : [0,1]×[0,1]→ [0,1] := I which is commutative, associative, monotone in each place, and has 1 as the unit element. Basic examples are TL : I × I → I , TL(a,b) =Max(a+ b− 1,0) (Łukasiewicz t-norm), TP(a,b) = ab, and TM(a,b) = Min{a,b}. We also mention the following families of tnorms: (i) Sugeno-Weber family (T λ )λ∈(−1,∞),...

Transitivity is a very important property in order to provide coherence to a preference relation. Usually, t-norms are considered to define the transitivity of fuzzy relations. In this paper we deal with conjunctors, a wider family than t-norm, to define the transitivity. This more general definition allows to impove the results found in the literature. We characterize the behaviour with respec...

The law of importation for fuzzy implications is studied and it is solved for S, R, QL and D-implications derived from uninorms. Along this study many new solutions of this property appears different from those already known for implications derived from t-norms and t-conorms.

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.