Fuzzy logic in narrow sense: A summary on t-norm-based logics In the seventies and eighties operations over [0,1] corresponding to connectives of a multi-valued logic has been studied and used to define Fuzzy Set operations. From then t-norms, t-conorms, negation and implication functions have been widely studied and applied. The nineties were the start point of the study of the kernel of fuzzy...

The composition of fuzzy relations for their uniting in multicriteria decision making problems is considered. Some criteria evaluate a set of alternatives by fuzzy preference relations. The comparison between the criteria importance is given as a fuzzy preference relation too. Aggregation of these relations is made with the help of a composition of the couple of the relations by the criteria an...

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...

Recently, many works have appeared dealing with the distributivity of fuzzy implications over t-norms, tconorms and uninorms (see [2, 3, 4, 5, 12, 13, 14]). These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems (see [6]). In this work we present some results connected with two functional equations describing the di...

There are presented the basic operations on real intervals: pseudo-addition and pseudo multiplication which induce the semiring structure. Application of special pseudo-operations on the unit interval: t-norms and t-conorms, in the theory of fuzzy sets and fuzzy logics are given. Pseudo-convolution as a generalization of the classical convolution is given, with many important special cases. Fur...

It is proposed in [Extension of Fuzzy Logic Operators Defined on Bounded Lattices via Retractions, Computer & Mathematics with Applications, 63: 1026–1038, 2012] a method for extending t-norms, t-conorms and fuzzy negations from a sublattice M of bounded lattice L considering a relaxed notion of sublattices. In this work we apply this method to extend a class of fuzzy negations constructed from...

The objective of this paper is to establish a class of models for solving the weight problem in fuzzy logic. First, some constraints that weighted fuzzy logic should satisfy are given based on Triangular norms and conorms. Then, based on these constraints, a class of models (referred to as relative weighted models) are established for handling weights in fuzzy logic. These models are novel in t...

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed ...

Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An aarmative answer to the question whether in such logics a speciic level of satissability of a set of formulas can be characterized by the same level of satissability of its nite subsets is given. Tautologies, contradictions and contingencies with respect to such fuzzy logics are studied, in particular fo...