We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide ...

The genetic algorithm behaviour is determined by the exploitation and exploration relationship kept throughout the run. Adap-tive genetic algorithms have been built for inducing suitable exploitation/exploration relationships for avoiding the premature convergence problem. Some adaptive genetic algorithms are built using fuzzy logic techniques. In this paper, we summarize two types of such appr...

In the information retrieval field, Fuzzy Information Retrieval Systems (FIRSs) use the potential of fuzzy techniques to improve the retrieval activities. Some models of FIRSs employ weighted queries to enhance the representation of user information needs and fuzzy connectives to evaluate such queries. In our teaching experience we have observed that students have many problems to understand th...

Active Learning Method (ALM) is a soft computing method used for modeling and control based on fuzzy logic. All operators defined for fuzzy sets must serve as either fuzzy S-norm or fuzzy T-norm. Despite being a powerful modeling method, ALM does not possess operators which serve as S-norms and T-norms which deprive it of a profound analytical expression/form. This paper introduces two new oper...

In the paper the problem of mathematical properties of B-operations and weak WB-operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system des...

In this paper, we extend research done in max-min fuzzy neural networks in several important ways. We replace max and min operations used in the fuzzy operations by more general t-norms and co-norms, respectively. In addition, instead of the Łukasiewicz equivalence connective used in network of ReyesGarcia and Bandler, we employ in our hybridization a variety of equivalence connectives. We expl...

Chu spaces, which derive from the Chu construct of ∗-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assu...

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 Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...

In the paper aspects of negative information and of information symmetry in context of uncertain information processing is considered. Both aspects are presented in frames of fuzzy sets theory involved in data aggregation and decision making process. Asymmetry of classical fuzziness and its orientation to positive information are pointed out. The direct dependence of symmetry of uncertain infor...