Hesitant Fuzzy Sets Theory

verfasst von: Zeshui Xu

Verlag: Springer International Publishing

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) characterized by uncertain ("hesitant") information. Because of its clarity and self contained explanations, the book can also be adopted as a textbook from graduate and advanced undergraduate students.

Inhaltsverzeichnis

Frontmatter

Hesitant Fuzzy Aggregation Operators and Their Applications

Abstract

Since fuzzy set (Zadeh 1965) was introduced, several extensions have been developed, such as intutionistic fuzzy set (Atanassov 1986), type-2 fuzzy set (Dubois and Prade 1980; Miyamoto 2005), type- n fuzzy set (Dubois and Prade 1980), fuzzy multiset (Yager 1986; Miyamoto 2000) and hesitant fuzzy set (Torra and Narukawa 2009; Torra 2010; Zhu et al. 2012a). Intuitionistic fuzzy set has three main parts: membership function, non-membership function and hesitancy function.

Zeshui Xu

Distance, Similarity, Correlation, Entropy Measures and Clustering Algorithms for Hesitant Fuzzy Information

Abstract

Distance and similarity measures are fundamentally important in a variety of scientific fields such as decision making, pattern recognition, machine learning and market prediction, lots of studies have been done about this issue on fuzzy sets (Turksen and Zhong 1988; Liu 1992; Bustince 2000; Candan et al. 2000). Among them, the most widely used distance measures for two fuzzy sets are the Hamming distance, the normalized Hamming distance, the Euclidean distance, and the normalized Euclidean distance (Diamond and Kloeden 1994; Kacprzyk 1997; Chaudhuri and Rosenfeld 1999).

Zeshui Xu

Hesitant Preference Relations

Abstract

Fuzzy preference relations (Orlovsky 1978) (also known as reciprocal preference relation (Baets et al. 2006; Xu 2007b,f; Xu and Chen 2008b)) and multiplicative preference relations (Saaty 1980) are the most common tools to express the DMs’ preferences over alternatives in decision making. However, sometimes, to get a more reasonable decision result, a decision organization, which contains a lot of DMs (or experts), is authorized to provide the preferences by comparing each pair of alternatives using 0-1 scale, and when providing the degrees to which an alternative is superior to another, it is not very sure about a value but has hesitancy between several possible values. In such cases, these several possible values can be considered as a HFE, and a hesitant fuzzy preference relation is constructed when all the preferences over a set of alternatives are provided (Xia and Xu 2013).

Zeshui Xu

Hesitant Fuzzy MADM Models

Abstract

Multi-attribute decision making (MADM), which addresses the problem of making an optimal choice that has the highest degree of satisfaction from a set of alternatives that are characterized in terms of their attributes, is a usual task in human activities. In classical MADM, the assessments of alternatives are precisely known (Dyer et al. 1992; Stewart 1992).

Zeshui Xu

Backmatter

Titel: Hesitant Fuzzy Sets Theory
verfasst von: Zeshui Xu
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-04711-9
Print ISBN: 978-3-319-04710-2
DOI: https://doi.org/10.1007/978-3-319-04711-9