As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

In [13], an algebraic approach to the natural structure of domains of linguistic variables was introduced. In this approach, every linguistic domain can be interpreted as an algebraic structure called a hedge algebra. In this paper, a refinement structure of hedge algebras based on free distributive lattices generated by linguistic hedge operations will be examined in order to model structure o...

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Autoepistemic logic is an important formalism for nonmonotonic reasoning. It extends propositional logic by offering the ability to reason about an agent’s (lack of) beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming. Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity to which properties are satisfied. W...

Inference in classical logic is monotonic: if a conclusion can be derived from a set of premises, then no additional premises will ever invalidate this conclusion. However, commonsense reasoning has a nonmonotonic component. Human beings draw sensible conclusions from what they know, making default assumptions where needed. And if there is new information, we might reconsider previous conclusio...

We argue that under the stable model semantics default negation can be read as explicit with update. show dynamic logic programming which is based on negation, even in heads, interpreted a variant of updates only. As corollaries, we get an easy description generalized and normal where initially negated literals are updated. These results discussed respect to understanding logic.

This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web. More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified nonmonotonic negation), and probabilistic uncertainty in a uniform framework for the Semant...

One of the most well-known and extended data mining techniques is that of association rule mining, a helpful tool to discover relations between items present in sets of transactions. Nevertheless, in some other scenarios, another interesting issue is that of considering not only the possible relations involving presence of items, but the absence of them. The problem gets more complex when it is...

In Gödel fuzzy propositional logic, neither conjunction nor implication is expressible (definable) in terms of the remaining three logical connectives. In classical propositional logic, propositions are associated with two truth values 1 (truth) and 0 (falsity). In fuzzy logics further (intermediate) truth values lying between 0 and 1 are possible. Usually the truth values are linearly ordered ...

Genetic Fuzzy Systems (GFSs) are models capable of integrating accuracy and high comprehensibility in their results. In the case of GFSs for classification, more emphasis has been given to improving the “Genetic” component instead of its “Fuzzy” counterpart. This paper focus on the Fuzzy Inference component to obtain a more accurate and interpretable system, presenting the so-called Genetic Pro...