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...

The main aim of this paper is to summarize recent advances on some new classes of associative operations (uninorms, nullnorms, t-operators) used in fuzzy set theory.

Come with us to read a new book that is coming recently. Yeah, this is a new coming book that many people really want to read will you be one of them? Of course, you should be. It will not make you feel so hard to enjoy your life. Even some people think that reading is a hard to do, you must be sure that you can do it. Hard will be felt when you have no ideas about what kind of book to read. Or...

This paper presents a framework for fuzzy set theory in which fuzzy values are intervals.

In fuzzy set theory, similarity phenomenon is approached using so-called fuzzy equivalence relations. An important role in fuzzy modeling is played by similarity-based closure (called also the extensional hull). Intuitively, the degree to which an element x belongs to a similarity-based closure of a fuzzy set A is the degree to which it is true that there is an element y in A which is similar t...

For classical sets one has their cumulative hierarchy, and also the category SET of all sets and mappings as standard approaches toward the universe of all sets. We discuss the corresponding situation for fuzzy set theory and give is a (concise) survey of a lot of such approaches which have been offered in the past approximately 35 years.

Tommaso Flaminio Lluís Godo Siegfried Gottwald Erich Peter Klement

In this paper, some earlier results dealing with fuzzy relations on fuzzy sets by one of the present authors are recapitulated to clarify the motivational background of the present study. Then concepts like fuzzy homorelation, correlation, cohomorelation, fuzzy function and fuzzy morphism are introduced and discussed. The presentation is uniform and integrated in the sense that every concept is...

Ulrich Bodenhofer Bernard De Baets Erich Peter Klement Susanne Saminger-Platz