Dual Hesitant Fuzzy Sets

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual...

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Bibliographic Details
Published inJournal of applied mathematics Vol. 2012; no. 2012; pp. 1 - 13
Main Authors Zhu, Bin, Xia, Meimei, Xu, Zeshui
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2012
John Wiley & Sons, Inc
Wiley
Subjects
Epistemology
Forecasting
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Grounds
Information retrieval
Intervals
Mathematical analysis
Studies
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Summary:In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2012/879629