Axiomatic Fuzzy Set Theory and Its Applications [electronic resource] /
Liu, Xiaodong.author.
Pedrycz, Witold.author.
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.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references and index.
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.
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.
Applied mathematics.
Engineering mathematics.
Artificial intelligence.
Algebra.
Applications of Mathematics.
Artificial Intelligence.
Algebra.
Mathematical and Computational Engineering.

Studies in Fuzziness and Soft Computing