
Axiomatic Fuzzy Set Theory and Its Applications
Springer (Publisher)
Published on 21. October 2010
Book
Paperback/Softback
XVIII, 514 pages
978-3-642-10146-5 (ISBN)
Description
It is well known that "fuzziness"-informationgranulesand fuzzy sets as one of its formal manifestations- is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the "empirical-semantic" approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 2009
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XVIII, 514 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 29 mm
Weight
797 gr
ISBN-13
978-3-642-10146-5 (9783642101465)
DOI
10.1007/978-3-642-00402-5
Schweitzer Classification
Other editions
Additional editions

Xiaodong Liu | Witold Pedrycz
Axiomatic Fuzzy Set Theory and Its Applications
Book
04/2009
Springer
€160.49
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Persons
Content
Required Preliminary Mathematical Knowledge.- Fundamentals.- Lattices.- Methodology and Mathematical Framework of AFS Theory.- Boolean Matrices and Binary Relations.- AFS Logic, AFS Structure and Coherence Membership Functions.- AFS Algebras and Their Representations of Membership Degrees.- Applications of AFS Theory.- AFS Fuzzy Rough Sets.- AFS Topology and Its Applications.- AFS Formal Concept and AFS Fuzzy Formal Concept Analysis.- AFS Fuzzy Clustering Analysis.- AFS Fuzzy Classifiers.