The paper discusses some core topics which present open problems in the field of mathematical fuzzy logic and in the foundations of fuzzy set theory. It may reasonably be assumed that these problems shall have great influence for the future development of fuzzy logic within the next decade.

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval 0; 1]. There are only denu-merable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathemat...

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. In the last decade, mathematical fuzzy logic has been developed as a discipline studying formal many-valued systems arising from fuzzy set theory. In this paper we study to what extent different systems of fuzzy logic are paraconsistent, identifying which f...

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval 0; 1]. There are only denu-merable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathemat...

Fuzzy logic is a modeling method intended to formalize a mathematical approach to deal with these complex or ill-defined systems and is, therefore, a relatively new mathematical paradigm. Its basis is a consideration of overlapping sets and the definition of operators to manipulate these sets. According to Zadeh and Mamdani, fuzzy logic could be used to develop operational automatic control sys...

The Fuzzy Logic and the Fuzzy Control approach is an important Artificial Intelligence technique, which allows designing and developing “human-thinking” based, intelligent systems or applications that employ effective mathematical calculations to solve real-world based problems. At this point, the related technique is widely used by scientists, researchers and engineers in different disciplines...

This paper deals with the design of fuzzy logic controller for dc – dc controllers. Fuzzy systems can be considered as a type of nonlinear function interpolator. The design of fuzzy controllers does not require an exact mathematical model. Instead they are designed based on general knowledge of the plant. Fuzzy logic controller (FLC) is cheaper to develop, they cover a wider range of operating ...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

A core tool for granular modeling is the use of linguistic rules, e.g. in fuzzy control approaches. We provide the reader with basic mathematical tools to discuss the behavior of system of such linguistic rules. These mathematical tools range from fuzzy logic and fuzzy set theory, through the consideration of fuzzy relation equations, up to discussions of interpolation strategies and to the use...