April 2019
Intermediate to advanced
304 pages
7h 12m
English
Content preview from Fuzzy Set and Its Extension
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Preface
Since Lofti A. Zadeh introduced fuzzy set theory about 50 years ago, i.e. in 1965, theory of fuzzy sets has evolved in many directions and has received more attention from many researchers. Applications of the theory can be found ranging from pattern recognition, control system, image processing, decision making, operations research, robotics, and management.
This book discusses on connections between fuzzy set and crisp set, fuzzy relations, operations on fuzzy sets, various aggregation operators using fuzzy sets, fuzzy numbers, arithmetic operations on fuzzy numbers, fuzzy integrals, fuzzy matrices and determinants, and fuzzy groups. Applications on decision making and image processing is also given.
Apart from fuzzy set, intuitionistic fuzzy set is also discussed in this book. Since its inception by K. Atanassov in 1985, intuitionistic fuzzy set theory has also received attention but to limited number of researchers as compared to fuzzy set. Though its use in application is not as comparable as that of fuzzy set, but still research studies are carried out in the areas that use fuzzy set. In intuitionistic fuzzy set, computational complexity is more as two types of uncertainties are used. But, for obtaining better result, where uncertainty present is more, especially in diagnosis of medical images, accurate result is very much important compromising the computational complexity. So, researchers try to use it on real‐time application.
The book discusses the basics ...
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