During the past decades, fuzzy logic control (FLC) has been one of the most active and fruitful areas for research in the application of fuzzy set theory. It has has been an active research topic in automation and control theory, since the work of Mamdani proposed in 1974 based on the fuzzy sets theory of Zadeh (1965), to deal with the system control problems which is not easy to be modeled [Ma...

The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real an...

In this paper we extend some results concerning ideals of left regular and intra-regular ordered semigroups to fuzzy ordered semigroups. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoidssemigroups have been already given by the same authors. The aim of writing this paper is to show the way we pass from the theory of ordered se...

For a class of uncertain nonlinear systems, this paper presents a method based on biological adaptation strategies of hybrid adaptive fuzzy control method. The method in the controller design, the ecological niche theory function as a consequent of the fuzzy rule fuzzy system, is established based on the biological adaptation of the adaptive controller. The controller design embodies the biolog...

The important growth of available multimedia information shows the limits of traditional information retrieval systems. In this paper, we describe the design of a metadata engine dedicated to retrieve annotated images using meta-information, and part of the more general MediaSys Image Search Engine. As a case study, we use medicinal plant images and their detailed description. We propose a flex...

The theory of neighborhood systems is abstracted from the geometric notion of "near" or "negligible distances." It is a "new" theory of the classical concept of neighborhood systems within the context of advanced computing. By definition neighborhood systems include both rough sets and topological spaces as special cases. The deeper and more interesting part is in its interactions with fuzzy se...

The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...

There are presented the basic operations on real intervals: pseudo-addition and pseudo multiplication which induce the semiring structure. Application of special pseudo-operations on the unit interval: t-norms and t-conorms, in the theory of fuzzy sets and fuzzy logics are given. Pseudo-convolution as a generalization of the classical convolution is given, with many important special cases. Fur...

Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor—the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the idea of a state of a system as a solution of fuzzy molecules, that is molecules that are not just different but rather similar, that react according to a set of ...