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We present a brief introduction to the theory of fuzzy sets and systems for readers who are not yet familiar with this powerful formal apparatus meant for the representation and processing of imprecisely specified (vague) concepts, descriptions, relations, etc. We show basic elements related to: the very concept of a fuzzy set, properties of fuzzy sets, operations on fuzzy sets, fuzzy relations, linguistic...
The chapter presents basic concepts and methods used in defining membership functions of fuzzy sets. Usual problems of fuzzy set applications connected with the universe of discourse, shape, and accuracy of membership functions as well as with their acquisition are discussed. An example of a fuzzy set application to a medical score test modelling is given. In the example a modified Takagi-Sugeno algorithm...
Fuzzy membership functions represent similarities of objects to ambiguous properties. All the information represented by a fuzzy set is contained within the membership function. This chapter summaries some methods to develop membership functions, briefly discusses the process of fuzzification (making crisp sets into fuzzy sets), and illustrates a few defuzzification (reducing fuzzy sets into singleton...
This paper provides an overview of some of the issues in using fuzzy sets for knowledge representation in computer systems. Since a fuzzy set is fully determined by its membership function the chief issues in fuzzy knowledge representation relate to how best to determine membership functions. A number of methods are discussed. However an alternative approach is to use type-2 fuzzy sets. Type-2 fuzzy...
This paper describes algebraic properties of fuzzy implications family and provides formulas for new fuzzy implications with their classification. First, we describe the lattice of fuzzy implications and its sublattices. Next, we examine properties of contrapositive and selfconjugate fuzzy implications. Finite sublattices are depicted by Hasse diagrams.
Machine learning (ML) algorithms have been capable of processing symbolic, categorial data only. Real-world problems, particularly in medicine, comprise not only symbolic, but also numerical attributes. There are several approaches to discretize (categorize) numerical attributes. This article describes two newer algorithms for such a discretization. The first one has been designed and implemented...
An overview of fuzzy clustering is given. The chapter starts with the definition of the basic notions of clustering and with a brief review of different approaches. Then, the focus is on fuzzy clustering based on the minimization of an objective function of the c-means type. Different algorithms are presented, including the Gustafson-Kessel algorithm, maximum-likelihood clustering, fuzzy c-varieties,...
Neurofuzzy systems are computing architectures whose main features arise as an effect of an important synergy occurring between two fundamental facets of information processing such as fuzzy computing and neurocomputing. Their underpinning is in a complementary character of fuzzy sets and neural networks. The latter is oriented toward more numeric processing of massive data. On the other hand, fuzzy...
This tutorial paper bas been written for physicians, biologists, more generally decision makers, who are beginners or little familiar with fuzzy sets theory and applications. The methodology that is presented is of special interest in the processing of borderline cases, allowing a graded assignment of diagnoses to patients or of professions to candidates (in vocational guidance systems). The field...
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