Xiaodong Liu, Witold Pedrycz (auth.)3642004016, 9783642004018, 9783642004025, 3642004024
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.
Table of contents :
Front Matter….Pages –
Front Matter….Pages 1-1
Fundamentals….Pages 3-60
Lattices….Pages 61-94
Front Matter….Pages 95-95
Boolean Matrices and Binary Relations….Pages 97-110
AFS Logic, AFS Structure and Coherence Membership Functions….Pages 111-166
AFS Algebras and Their Representations of Membership Degrees….Pages 167-224
Front Matter….Pages 225-225
AFS Fuzzy Rough Sets….Pages 227-267
AFS Topology and Its Applications….Pages 269-301
AFS Formal Concept and AFS Fuzzy Formal Concept Analysis….Pages 303-349
AFS Fuzzy Clustering Analysis….Pages 351-421
AFS Fuzzy Classifiers….Pages 423-489
Back Matter….Pages –
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