| Logical inference starts with concluding that if B implies A, and B is true, then A is true as well. To describe probabilistic inference rules, we must therefore deene the probability of an implication \A if B". There exist two diierent approaches to deening this probability, and these approaches lead to diierent probabilistic inference rules: We may interpret the probability of an implicatio...

The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...

In this paper we present interesting relationships between the context model, modal logic and fuzzy concept analysis. It has been shown that the context model proposed by Gebhardt and Kruse [Int. J. Approx. Reason. 9 (1993) 283] can be semantically extended and considered as a data model for fuzzy concept analysis within the framework of the meta-theory developed by Resconi et al. in 1990s. Con...

In this paper we deal with propositional fuzzy formulae containing several propositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. Instead of focusing on satisfiability (i.e., proving the existence of at least one model) as usually done in a SAT/SMT setting, our interest moves to the problem of finding the whole set of models (with a finite do...

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truthstressing and -depressing hedges as expansions of Hájek’s BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which h...

This paper is the continuation of [11] where the rotation construction of left-continuous triangular norms was presented. Here the class of triangular subnorms and a second construction, called rotation-annihilation, are introduced: Let T1 be a left-continuous triangular norm. If T1 has no zero divisors then let T2 be a left-continuous rotation invariant t-subnorm. If T1 has zero divisors then ...

The pattern recognition literature is replete with the use of principal component analysis in the interpretation and analysis of data. However, in the specific case of classification, especially of biomedical patterns, this pre-processing method, which transforms possibly correlated features into a new set of uncorrelated variables, must be used with caution since a principal component, which m...

Fuzzy control is a methodology that transforms control rules (described by an expert in words of a natural language) into a precise control strategy. There exist several versions of this transformation. The main difference between these versions is in how they interpret logical connectives “and” and “or”, i.e., in other words, what reasoning method a version uses. Which of these versions should...

A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain e:z:pert 's knowledge is e:z:pressed by a set of rules that frequently refer to vague and uncertain propositions. Th.e certainty of propositions is represented using intervals {a. bj e:z:pressing that the proposition's probability is at least a and at most b. Methods and techniques f...

Fuzzy logic is one of the tools for management of uncertainty; it works with more than two values, usually with a continuous scale, the real interval [0,1]. Implementation restrictions in applications force us to use in fact a finite scale (finite chain) of truth degrees. In this paper, we study logical operations on finite chains, in particular conjunctions. We describe a computer program gene...