Bahram Farhadinia - Hesitant Fuzzy Set: Theory and Extension

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Hesitant fuzzy set has moved beyond its infancy and is now entering a maturing phase with increased numbers and types of extensions. Up to now, the existing extensions of hesitant fuzzy set have been encountering an increasing interest and attracting more and more attentions. It is not an exaggeration if it is said that the recent decade has seen the blossoming of a larger set of techniques and theoretical outcomes for hesitant fuzzy sets and their extensions as well as applications.

Inevitably, researches on hesitant fuzzy set and its extensions have inspired a huge amount of publications, including a considerable number of high-impact journal contributions, numerous edited volumes, and monographs. This is while, in spite of the existence of many good monographs, creating a comprehensive book that covers and introduces all kinds of exiting extensions of hesitant fuzzy sets in a unified framework has remained a little neglected or ignored. Thus, it is becoming more and more necessary to gather and provide an organized and rather unified view of these extensions and their key notions, with reference to the relevant literature.

According to the feedback from several experts and based on my own experience gained through the past ten years, the main motivation of writing this book is to provide the students, scholars, and interested readers with a monograph that covers all kinds of exiting hesitant fuzzy extensions in a unified scheme. Further, I hope that this all-encompassing reference book enables scientists and engineers to understand the central aspects of hesitant fuzzy extensions.

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 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 , 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.

Chapter is devoted to introducing briefly the concept of neutrosophic set in the first section. Subsequently, the concept of single-valued neutrosophic hesitant fuzzy set, which is refereed here to as neutrosophic hesitant fuzzy set, is addressed in the second section. In the sequel, it is going to argue about the concept of interval neutrosophic hesitant fuzzy set. Although there may be reported some other kinds of neutrosophic hesitant fuzzy set by different researchers, the aforementioned two types of neutrosophic-based hesitant fuzzy sets are enough to fully understand the other kinds.