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This book generalizes fuzzy logic systems for different types of uncertainty, including
- semantic ambiguity resulting from limited perception or lack of knowledge about exact membership functions
- lack of attributes or granularity arising from discretization of real data
- imprecise description of membership functions
- vagueness perceived as fuzzification of conditional attributes.
Consequently, the membership uncertainty can be modeled by combining methods of conventional and type-2 fuzzy logic, rough set theory and possibility theory.
In particular, this book provides a number of formulae for implementing the operation extended on fuzzy-valued fuzzy sets and presents some basic structures of generalized uncertain fuzzy logic systems, as well as introduces several of methods to generate fuzzy membership uncertainty. It is desirable as a reference book for under-graduates in higher education, master and doctor graduates in the courses of computer science, computational intelligence, or fuzzy control and classification, and is especially dedicated to researchers and practitioners in industry.
List of contents
Uncertainty in Fuzzy Sets.- Algebraic Operations on Fuzzy Valued Fuzzy Sets.- Defuzzification of Uncertain Fuzzy Sets.- Generalized Uncertain Fuzzy Logic Systems.- Uncertainty Generation in Uncertain Fuzzy Logic Systems.- Designing Uncertain Fuzzy Logic Systems.
Summary
This book generalizes fuzzy logic systems for different types of uncertainty, including
- semantic ambiguity resulting from limited perception or lack of knowledge about exact membership functions
- lack of attributes or granularity arising from discretization of real data
- imprecise description of membership functions
- vagueness perceived as fuzzification of conditional attributes.
Consequently, the membership uncertainty can be modeled by combining methods of conventional and type-2 fuzzy logic, rough set theory and possibility theory.
In particular, this book provides a number of formulae for implementing the operation extended on fuzzy-valued fuzzy sets and presents some basic structures of generalized uncertain fuzzy logic systems, as well as introduces several of methods to generate fuzzy membership uncertainty. It is desirable as a reference book for under-graduates in higher education, master and doctor graduates in the courses of computer science, computational intelligence, or fuzzy control and classification, and is especially dedicated to researchers and practitioners in industry.
Additional text
From the reviews:
“This monograph brings an overview of the theory of type-2 fuzzy set theory, reasoning using rough approximations of fuzzy sets and constructions of fuzzy logic systems … . The book brings a sound mathematical background to treat a serious processing of uncertainty, respecting the properties of fuzzy sets important for engineering applications and for their sound uncertain extensions. … can be recommended for any reader interested in fuzzy set theory but especially for researchers working with uncertain information, including PhD students.” (Radko Mesiar, Zentralblatt MATH, Vol. 1254, 2013)
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From the reviews:
"This monograph brings an overview of the theory of type-2 fuzzy set theory, reasoning using rough approximations of fuzzy sets and constructions of fuzzy logic systems ... . The book brings a sound mathematical background to treat a serious processing of uncertainty, respecting the properties of fuzzy sets important for engineering applications and for their sound uncertain extensions. ... can be recommended for any reader interested in fuzzy set theory but especially for researchers working with uncertain information, including PhD students." (Radko Mesiar, Zentralblatt MATH, Vol. 1254, 2013)
