Counting of finite fuzzy subsets with applications to fuzzy recognition and selection strategies

The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets with same features, characteristics or conditions. To facilitate such a study, we use some ideas such as the Hamming distance, mid-point between two fuzzy subsets and cardinality of fuzzy subsets. Finally we introduce the fuzzy scanner of elements of a finite set. This is used to identify elements and fuzzy subsets of a set. The scanning process of identification and recognition facilitates the choice of entities with specified properties. We develop a procedure of selection under the fuzzy environment. This allows us a framework to resolve conflicting issues in the market place

Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.Comment: 13 page

Synthesis of nonlinear control strategies from fuzzy logic control algorithms

Fuzzy control has been recognized as an alternative to conventional control techniques in situations where the plant model is not sufficiently well known to warrant the application of conventional control techniques. Precisely what fuzzy control does and how it does what it does is not quite clear, however. This important issue is discussed and in particular it is shown how a given fuzzy control scheme can resolve into a nonlinear control law and that in those situations the success of fuzzy control hinges on its ability to compensate for nonlinearities in plant dynamics

Fuzzy Controller for Matrix Converter System to Improve its Quality of Output

In this paper, Fuzzy Logic controller is developed for ac/ac Matrix Converter. Furthermore, Total Harmonic Distortion is reduced significantly. Space Vector Algorithm is a method to improve power quality of the converter output. But its quality is limited to 86.7%.We are introduced a Cross coupled DQ axis controller to improve power quality. The Matrix Converter is an attractive topology for High voltage transformation ratio. A Matlab / Simulink simulation analysis of the Matrix Converter system is provided. The design and implementation of fuzzy controlled Matrix Converter is described. This AC-AC system is proposed as an effective replacement for the conventional AC-DC-AC system which employs a two-step power conversion.Comment: 11 page