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farhadinia b hesitant fuzzy set theory extension 2021

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Textbook in PDF format Covering a wide range of notions concerning hesitant fuzzy set and its extensions, this book provides a comprehensive reference to the topic. In the case where different sources of vagueness appear simultaneously, the concept of fuzzy set is not able to properly model the uncertainty, imprecise and vague information. In order to overcome such a limitation, different types of fuzzy extension have been introduced so far. Among them, hesitant fuzzy set was first introduced in 2010, and the existing extensions of hesitant fuzzy set have been encountering an increasing interest and attracting more and more attentions up to now. It is not an exaggeration to say that the recent decade has seen the blossoming of a larger set of techniques and theoretical outcomes for hesitant fuzzy set together with its extensions as well as applications. This book gives preliminary, but fundamental, information that may be useful for a better understanding of hesitant fuzzy extensions in a unified framework. The current book is organized into twelve chapters that deal with twelve different but related issues, which are listed as follows: Chapter 1 provides the readers with further background on hesitant fuzzy set as the core concept of this book, and fundamental information bases for the study of direct generalized forms of hesitant fuzzy set. In this regard, the basic operational laws, fundamental definitions, basic operations, different kinds of negations, S-norms, and T-norms together with two kinds of ordering techniques for hesitant fuzzy sets are presented in the first section of this chapter. The other section of this chapter deals with the direct extensions of hesitant fuzzy sets just by representing their basic concepts in brief together with their corresponding set or algebraic operations. Most popular among these direct generalizations are the hesitant triangular fuzzy set, interval-valued hesitant fuzzy set, extended hesitant fuzzy set, higher order of hesitant fuzzy set, dual hesitant fuzzy set, dual hesitant triangular fuzzy set, and interval-valued dual hesitant fuzzy set. Chapter 2, in the first section, initially introduces the concept of hesitant fuzzy linguistic term set that reflects the inconsistency and uncertainty of experts. Then, the extended form of hesitant fuzzy linguistic term set, namely extended hesitant fuzzy linguistic term set, is re-stated and a number of its operations are reviewed. In the sequel, the interval-valued hesitant fuzzy linguistic term set is taken into consideration in the third section. In the fifth and fourth sections, the concepts of proportional hesitant fuzzy linguistic term set and hesitant fuzzy uncertain linguistic set are, respectively, addressed. The concept of dual hesitant fuzzy linguistic term set, which allows us to take much more information into account, is reviewed in the sixth section. Two other generalized forms of hesitant fuzzy linguistic term set, which are known as dual hesitant fuzzy linguistic triangular set and interval-valued dual hesitant fuzzy linguistic set, are the issues that lie at the end arguments in this chapter

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farhadinia b hesitant fuzzy set theory extension 2021