Axiomatic Fuzzy Set Theory And Its Applications Pdf

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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. Pedrycz Published in Studies in Fuzziness and Soft…. View via Publisher.

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. The material can be found equally advantageous to the readers involved in the theory and practice of fuzzy sets as well as those interested in mathematics, rough sets, granular computing, formal concept analysis, and the use of probabilistic methods.

It seems that you're in Germany. We have a dedicated site for Germany. Authors: Liu , Xiaodong, Pedrycz , Witold. 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.

Set theory

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. In the last section of the paper, we present our interpretations on the future of fuzzy sets.

Set theory is a branch of mathematical logic that studies sets , which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the s. After the discovery of paradoxes in naive set theory , such as Russell's paradox , numerous axiom systems were proposed in the early twentieth century, of which the Zermelo—Fraenkel axioms , with or without the axiom of choice , are the best-known.

A generalization to n-ary relations is straightforward. Customer decision making CDM is an indispensable factor for e-business and Web services. Obviously, Y X, so 2P. Join ResearchGate to find the people and research you need to help your work. Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. Many more concepts and theories could not be discussed, either because of space limitations, because they cannot yet be considered ready for a textbook, or they are too specific and advanced for the goal of this textbook. Rather than specifying here which of the numerous definitions we accept, or introducing an additional definition, we shall just mention a number of features of expert systems, which might be accepted by most designers and users of expert systems and which seem to be of relevance with respect to fuzzy sets: I hope, however, that after studying this book the reader will be in a position to read, understand and evaluate most of the papers and books that are being published now.


Buy this book. eBook ,09 €. price for Spain (gross). Buy eBook. ISBN ​; Digitally watermarked, DRM-free; Included format: PDF; ebooks can.


set theory textbook pdf

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. Various distance measures on IFSs have been developed by many researchers and used in medical diagnosis in last few decades. Medical diagnosis is one of the major decision-making situation in medical science. From the existing research and knowledge in medical science, the major, as well as minor symptoms of almost all disease, are recorded.

Set theory

 Никаких изменений. Внезапно Мидж судорожно указала на экран. - Смотрите. На экран выплыла надпись: КЛЮЧ К ШИФРУ-УБИЙЦЕ ПОДТВЕРЖДЕН - Укрепить защитные стены! - приказал Джабба. Но Соши, опередив его, уже отдала команду.

Тот, конечно, был мастером своего дела, но наемник остается наемником. Можно ли ему доверять. А не заберет ли он ключ. Фонтейну нужно было какое-то прикрытие - на всякий случай, - и он принял необходимые меры.

Однако Беккер был слишком ошеломлен, чтобы понять смысл этих слов. - Sientate! - снова крикнул водитель.

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