scispace - formally typeset
Search or ask a question
Journal Article•DOI•

Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making

Zhiming Zhang1•
Hebei University1
01 Jun 2013-Information Sciences (Elsevier Science Inc.)-Vol. 234, pp 150-181
TL;DR: This paper develops a wide range of hesitant fuzzy power aggregation operators for hesitant fuzzy information and demonstrates several useful properties of the operators and discusses the relationships between them.
About: This article is published in Information Sciences.The article was published on 2013-06-01. It has received 304 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.
Citations
More filters
Journal Article•DOI•
Hesitant Fuzzy Sets: State of the Art and Future Directions

[...]

Rosa M. Rodríguez1, Luis Martínez1, Vicenç Torra, Zeshui Xu2, Francisco Herrera3, Francisco Herrera4 •
University of Jaén1, Sichuan University2, University of Granada3, King Abdulaziz University4
01 Jun 2014-Journal of intelligent systems
TL;DR: An overview on hesitant fuzzy sets is presented with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.
Abstract: The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.

405 citations

Cites background from "Hesitant fuzzy power aggregation op..."

  • ...A variety of Hesitant Fuzzy Power aggregation operators and their relationships have been introduced in [23, 67]....

    [...]

  • ...Diverse extensions and generalizations of these two operators were also presented in [23, 67]....

    [...]

Journal Article•DOI•
Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

[...]

Jian-qiang Wang1, Jia-ting Wu1, Jing Wang1, Hong-yu Zhang1, Xiaohong Chen1 •
Central South University1
20 Dec 2014-Information Sciences
TL;DR: This work focuses on multi-criteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of interval-valued hesitant fuzzy linguistic numbers (IVHFLNs).

310 citations

Cites background from "Hesitant fuzzy power aggregation op..."

  • ...Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.07.034 Jian-qiang Wang ⇑, Jia-ting Wu, Jing Wang, Hong-yu Zhang, Xiao-hong Chen School of Business, Central South University, Changsha 410083, China 24 25 26 27 28 29 30 31 32 33 34 a r t i c l e i n f o Article history: Received 16 April 2014 Received in revised form 18 July 2014 Accepted 27 July 2014 Available online xxxx Keywords: Multi-criteria decision-making Interval-valued hesitant fuzzy linguistic set Linguistic scale function Prioritized aggregation operator 35 36 37 38 39 a b s t r a c t An interval-valued hesitant fuzzy linguistic set (IVHFLS) can serve as an extension of both a linguistic term set and an interval-valued hesitant fuzzy set....

    [...]

  • ...Recently, Rodríguez et al. [43] presented an overview and discussed future trends for HFSs. Farhadinia [12] proposed a series of score functions for HFSs. Wei [57], Zhang [81], Yu [74], and Ai et al. [1] studied the aggregation operators of HFSs. Farhadinia [11], Xu and Xia [68], Peng et al. [37], and Chen et al. [7] discussed the information measures of HFSs. Hesitant fuzzy TOPSIS [69] and hesitant fuzzy criteria 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 2 J.-q. WanQ1 g et al. / Information Sciences xxx (2014) xxx–xxx Q1 TODIM [80] methods for solving MCDM problems have been proposed....

    [...]

  • ...Therefore, similarly to Zhang [79], the method used for ranking is why the ranking result obtained by [53] is not the same, that is, ranking by the expected values is better than ranking by the score function values....

    [...]

  • ...Wei [57], Zhang [81], Yu [74], and Ai et al....

    [...]

  • ...However, according to Zhang [79], if the expected values are used to rank the alternatives, x5 x1 x3 x2 x4 is obtained, which is the same ranking as some of the results obtained by the proposed method, i.e. the first and third semantic situations....

    [...]

Journal Article•DOI•
Possibility Distribution-Based Approach for MAGDM With Hesitant Fuzzy Linguistic Information

[...]

Zhibin Wu1, Jiuping Xu1•
Sichuan University1
01 Mar 2016-IEEE Transactions on Systems, Man, and Cybernetics
TL;DR: A new framework model to address multiple attribute GDM with hesitant fuzzy linguistic information, which uses different identification and direction rules compared with the existing methods to support stakeholders when making rational decisions is presented.
Abstract: In group decision making (GDM) with qualitative settings, experts may require several possible linguistic values rather than a single term to express their preferences. A hesitant fuzzy linguistic term set has recently been developed to manage this situation. In line with this development, in this paper, we present a new framework model to address multiple attribute GDM with hesitant fuzzy linguistic information. First, the concept of a possibility distribution is defined. Based on the possibility distributions, some aggregation operators such as the hesitant fuzzy linguistic weighted average operator and the hesitant fuzzy linguistic ordered weighted average operator are proposed. A consensus measure is then defined and a consensus reaching process is given which uses different identification and direction rules compared with the existing methods. A selection process is also described to rank the alternatives. Both processes are necessary to support stakeholders when making rational decisions. Finally, two simulated examples are given to verify the practicability of the proposed approach.

265 citations

Additional excerpts

  • ...hesitant situations (see [49], [51], [60], [62], amongst others)....

    [...]

Journal Article•DOI•
Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information

[...]

Jian-qiang Wang1, Lu Peng1, Hong-yu Zhang1, Xiaohong Chen1•
Central South University1
01 Aug 2014-Information Sciences
TL;DR: A linguistic multi-criteria group decision-making method is developed that converts linguistic variables into clouds and then aggregated using cloud aggregation operators, and is compared to existing methods to confirm its feasibility and rationality.

229 citations

Journal Article•DOI•
Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making

[...]

José M. Merigó1, Anna M. Gil-Lafuente•
University of Manchester1
01 Jul 2013-Information Sciences
TL;DR: The induced 2-tuple linguistic generalized ordered weighted averaging (2-TILGOWA) operator is presented and the applicability of this new approach in a multi-person linguistic decision-making problem concerning product management is analysed.

211 citations

References
More filters
Book•
Fuzzy sets

[...]

Lotfi A. Zadeh
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal Article•DOI•
Intuitionistic fuzzy sets

[...]

Krassimir T. Atanassov1•
Bulgarian Academy of Sciences1
01 Aug 1986-Fuzzy Sets and Systems
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

"Hesitant fuzzy power aggregation op..." refers background in this paper

  • ...Several classical extensions of the concept have been developed, including the interval-valued fuzzy set [37,64], intuitionistic fuzzy set [2,3,23,25], intervalvalued intuitionistic fuzzy set [4,22,41], linguistic fuzzy set [46,48], type-2 fuzzy set [5,10,12–14,30,66], type-n fuzzy set [10], and fuzzy multiset [29,61]....

    [...]

Journal Article•DOI•
The concept of a linguistic variable and its application to approximate reasoning—II☆

[...]

Lotfi A. Zadeh1•
University of California1
01 Jan 1975-Information Sciences
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.

12,530 citations

The Concepts of a Linguistic Variable and its Application to Approximate Reasoning

[...]

Lotfi A. Zadeh
01 Jan 1975

8,942 citations

"Hesitant fuzzy power aggregation op..." refers background in this paper

  • ...Several classical extensions of the concept have been developed, including the interval-valued fuzzy set [37,64], intuitionistic fuzzy set [2,3,23,25], intervalvalued intuitionistic fuzzy set [4,22,41], linguistic fuzzy set [46,48], type-2 fuzzy set [5,10,12–14,30,66], type-n fuzzy set [10], and fuzzy multiset [29,61]....

    [...]

  • ...In practice, we often encounter situations in which the input arguments cannot be expressed as exact numerical values; instead, they might take the form of interval numbers [60], intuitionistic fuzzy numbers [6,7,15,42,58], interval-valued intuitionistic fuzzy numbers [51], linguistic variables [1,8,9,16,17,24,28,31,32,39,64,65,69], uncertain linguistic variables [26,47,49,50], or 2-tuples [18–20,27]....

    [...]

Book•
Fuzzy Sets and Systems: Theory and Applications

[...]

Didier Dubois, Henri Prade
01 Jan 2011
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Abstract: (1982). Fuzzy Sets and Systems — Theory and Applications. Journal of the Operational Research Society: Vol. 33, No. 2, pp. 198-198.

5,861 citations

Related Papers (5)
Hesitant fuzzy information aggregation in decision making

[...]

01 Mar 2011-International Journal of Approximate Reasoning
Meimei Xia, Zeshui Xu
Hesitant fuzzy sets

[...]

01 Jun 2010-Journal of intelligent systems
Vicenç Torra
Distance and similarity measures for hesitant fuzzy sets

[...]

01 Jun 2011-Information Sciences
Zeshui Xu, Meimei Xia
Intuitionistic fuzzy sets

[...]

01 Aug 1986-Fuzzy Sets and Systems
Krassimir T. Atanassov
Fuzzy sets

[...]

01 Aug 1996
Lotfi A. Zadeh