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Axiomatic Fuzzy Set Theory And Its Applications Pdf

axiomatic fuzzy set theory and its applications pdf

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Set theory

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set theory textbook pdf

In the age of Machine Intelligence and computerized decision making, we have to deal with subjective imprecision inherently associated with human perception and described in natural language and uncertainty captured in the form of randomness. This treatise develops the fundamentals and methodology of Axiomatic Fuzzy Sets AFS , in which fuzzy sets and probability are treated in a unified and coherent fashion. It offers an efficient framework that bridges real world problems with abstract constructs of mathematics and human interpretation capabilities cast in the setting of fuzzy sets. In the self-contained volume, the reader is exposed to the AFS being treated not only as a rigorous mathematical theory but also as a flexible development methodology for the development of intelligent systems. The way in which the theory is exposed helps reveal and stress linkages between the fundamentals and well-delineated and sound design practices of practical relevance. The algorithms being presented in a detailed manner are carefully illustrated through numeric examples available in the realm of design and analysis of information systems.

Axiomatic Fuzzy Set Theory and Its Applications

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Liu and W. Liu , W.

Set theory is a branch of mathematical logic that studies sets , which informally are collections of objects.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Possibility theory and its applications: a retrospective and prospective view Abstract: This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and nonmonotonic reasoning.

Decision making in medical diagnosis is becoming a vast research field in medical science. In the last few decades, the role of distance measure in decision science is significant.

Fuzzy sets have a great progress in every scientific research area. It found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. In this paper, a comprehensive literature review on the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. This literature review also analyzes the chronological development of these extensions.

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