In intelligent systems where fuzzy rule base and reasoning mechanism are applied, like fuzzy control systems, decision support and expert systems, one of the key issues is the problem of aggregation of information represented by membership functions. Since the pioneering work of Prof. Lotfi Zadeh [21] a great number of fuzzy connectives, aggregation operators have been introduced. The results o...

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inc...

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...

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inc...

In some knowledge domains, a correct handling of vagueness and imprecision is fundamental for adequate knowledge representation and reasoning. For example, when trying to diagnose a disease, medical experts need to confront symptoms described by the patient, which are by definition subjective, and hence vague. Moreover, a single malady may present a diversity of clinical manifestations in diffe...

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...

During the last years, we have developed the  platform for providing a practical support to the so-called Multi-Adjoint Logic Programming approach (MALP in brief), which represents an extremely flexible framework into the Fuzzy Logic Programming arena. Nowadays,  is useful for compiling (to standard Prolog code), executing and debugging (by drawing execution trees) MALP programs, an...

FASILL (acronym of “Fuzzy Aggregators and Similarity Into a Logic Language”) is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi∼Prolog (which u...

Active Learning Method (ALM) is a soft computing method which is used for modeling and control, based on fuzzy logic. Although ALM has shown that it acts well in dynamic environments, its operators cannot support it very well in complex situations due to losing data. Thus ALM can find better membership functions if more appropriate operators be chosen for it. This paper substituted two new oper...

Each fuzzy set can be represented by a nested system of ordinary sets—its a-cuts. There is an extensive literature on fuzzy sets devoted to problems of the following kind: is it possible to reduce operations with fuzzy sets to operations with their a-cuts? Is it possible to reduce properties of fuzzy relations to properties of their a-cuts? More generally, can a fuzzy concept be represented by ...