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Necessary and possible hesitant fuzzy sets: A novel model for group decision making

Published on Mar 1, 2019in Information Fusion10.716
· DOI :10.1016/j.inffus.2018.05.005
José Carlos R. Alcantud19
Estimated H-index: 19
(University of Salamanca),
Alfio Giarlotta11
Estimated H-index: 11
(University of Catania)
Sources
Abstract
Abstract We propose an extension of Torra’s notion of hesitant fuzzy set, which appears to be well suited to group decision making. In our model, indecisiveness in judgements is described by two nested hesitant fuzzy sets: the smaller, called necessary, collects membership values determined according to a rigid evaluation, whereas the larger, called possible, comprises socially acceptable membership values. We provide several instances of application of our methodology, and accordingly design suitable individual and group decision procedures. This novel approach displays structural similarities with Atanassov’s intuitionistic fuzzy set theory, but has rather different goals. Our source of inspiration comes from preference theory, where a bi-preference approach has proven to be a useful extension of the classical mono-preference modelization in the fields of decision theory and operations research.
  • References (51)
  • Citations (20)
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References51
Newest
#1José Carlos R. Alcantud (University of Salamanca)H-Index: 19
#2Alessio Emanuele Biondo (University of Catania)H-Index: 9
Last. Alfio Giarlotta (University of Catania)H-Index: 11
view all 3 authors...
Abstract We propose a novel modelization of the party formation process, in which citizens' private opinions are described by means of continuous fuzzy profiles. Those citizens who show a high level of commitment become politicians, and create a public profile of political tolerance that extends their private profile. The main goal of this first paper is to describe how parties endogenously emerge from the matching mechanism of the private-and-public profiles of politicians. We provide an algori...
8 CitationsSource
#1Dengbao Yao (Anda: Anhui University)H-Index: 1
#2Cuicui WangH-Index: 1
In this paper, we introduce a new concept of hesitant intuitionistic fuzzy set (HIFS), which refines the dual hesitant fuzzy set and could be viewed as a more flexible tool to describe the uncertain information in reality. Since the uncertainty in HIFSs may be divided into three facets: fuzziness, intuitionism and hesitancy, we develop a fresh information-theoretic framework of uncertainty measures. We firstly propose the axiomatic principles of hesitant intuitionistic fuzzy entropy and give som...
2 CitationsSource
#1José Carlos R. Alcantud (University of Salamanca)H-Index: 19
#2Vicenç Torra i Reventós (University of Skövde)H-Index: 36
36 CitationsSource
#1Alfio Giarlotta (University of Catania)H-Index: 11
#2Stephen Watson (York University)H-Index: 11
Abstract The transitivity of a preference relation is a traditional tenet of rationality in economic theory. However, several weakenings of transitivity have proven to be extremely useful in applications, giving rise to the notions of interval orders and semiorders among others. Strict ( m , 1 ) -Ferrers properties go in this direction, classifying asymmetric preferences on the basis of their degree of transitivity, which becomes generally weaker as m gets larger. We show that strict ( m , 1 ) -...
6 CitationsSource
#1Alfio Giarlotta (University of Catania)H-Index: 11
#2Stephen Watson (York University)H-Index: 11
Abstract A NaP-preference (necessary and possible preference) is a pair of nested reflexive relations on a set such that the smaller is transitive, the larger is complete, and the two relations jointly satisfy properties of transitive coherence and mixed completeness. It is known that a NaP-preference is characterized by the existence of a set of total preorders whose intersection and union give its two components. We introduce the symmetric counterpart of a NaP-preference, called a NaP-indiffer...
6 CitationsSource
#1Shen Zhang (Sichuan University)H-Index: 1
#2Zeshui Xu (Sichuan University)H-Index: 94
Last. Yue He (Sichuan University)H-Index: 1
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Propose the improved P-HFS and P-HFE.Develop some aggregation operators for the improved P-HFEs.Extend the improved P-HFEs to their continuous counterparts.Give the operations and distance measures for the continuous counterparts.Verify our results by a case study concerning the automobile safety evaluations. In recent years, the hesitant fuzzy set (HFS) has been widely applied in practical decision making processes. As a matter of fact, it indeed describes the thoughts of experts better because...
35 CitationsSource
#1José Carlos R. Alcantud (University of Salamanca)H-Index: 19
#2Gustavo Santos-García (University of Salamanca)H-Index: 7
We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example.
4 CitationsSource
#1Zhinan HaoH-Index: 5
#2Zeshui Xu (NUIST: Nanjing University of Information Science and Technology)H-Index: 94
Last. Zhan SuH-Index: 1
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Propose the concept of the probabilistic dual hesitant fuzzy set (PDHFS).Define the basic operational laws and some aggregation operators of the PDHFS for the information fusion.Propose the concept of entropy for the PDHFS and develop a visual analysis method for the aggregated results.Apply the proposed theory and methods to the Arctic geopolitical risk evaluation. The concurrence of randomness and imprecision widely exists in real-world problems. To describe the aleatory and epistemic uncertai...
29 CitationsSource
#1Bin Zhu (THU: Tsinghua University)H-Index: 16
#2Zeshui Xu (Sichuan University)H-Index: 94
AbstractHesitant fuzzy sets (HFSs) are a useful tool to manage situations in which the decision makers (DMs) hesitate about several possible values for the membership to assess a variable, alternative, etc. However, HFSs have the information loss problem and cannot identify different DMs, which interferes with the application of HFSs in decision making. To overcome these limitations, we develop the extended hesitant fuzzy sets (EHFSs) in this paper. As an extension of HFSs, EHFSs have close rela...
27 CitationsSource
#1Alfio Giarlotta (University of Catania)H-Index: 11
#2Stephen Watson (York University)H-Index: 11
Abstract A NaP-preference (necessary and possible preference) is a pair of nested reflexive relations on a set such that the smaller is transitive, the larger is complete, and the two components jointly satisfy natural forms of mixed completeness and transitive coherence. A NaP-preference is normalized if its smaller component is a partial order. We show that normalized NaP-preferences on a finite set are well-graded in the sense of Doignon and Falmagne (1997).
9 CitationsSource
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#1Xiaoyi MoH-Index: 1
#2Hua ZhaoH-Index: 11
Last. Zeshui Xu (Sichuan University)H-Index: 94
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Abstract Satisfaction with life scale is a comprehensive cognitive judgement of individual’s own life and becomes the dominant measure of life satisfaction. However, the individual may hesitate to assess his/her life satisfaction with a single value due to multiple criteria. Consequently, we propose the hesitant fuzzy satisfaction with life scale (HFSWLS) with the same form as hesitant fuzzy element (HFE), consisting of several possible values of the cognitive judgements to describe the uncertai...
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#1Mahdi Ranjbar (FUM: Ferdowsi University of Mashhad)H-Index: 4
#2Seyed Mohsen Miri (FUM: Ferdowsi University of Mashhad)H-Index: 1
Last. Sohrab Effati (FUM: Ferdowsi University of Mashhad)H-Index: 21
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Abstract In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study some essential properties of these numbers. We show (α, k)-cuts that were discussed in the recent literature for hesitant fuzzy sets (HFSs), on HFNs have resulted in compact intervals. In the following, we propose a new binary operation on these numbers. It has shown that the outcome of the proposed operation is a HFN. In addition, a new hesitant fuzzy relationship for comparing two HFNs is given. Fina...
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#1Alfio Giarlotta (University of Catania)H-Index: 11
#2Stephen Watson (York University)H-Index: 11
Abstract Consumers’ preferences and choices are traditionally described by appealing to two classical tenets of rationality: transitivity and completeness. In 1971, Schmeidler proved a striking result on the interplay between these properties: On a connected topological space, a nontrivial bi-semicontinuous preorder is complete. Here we reformulate and extend this well-known theorem. First, we show that the topology is not independent of the preorder, contrary to what the original statement sugg...
3 CitationsSource
#1Xue Chen (Sichuan University)
#2Lijie Peng (Sichuan University)
Last. Witold Pedrycz (U of A: University of Alberta)H-Index: 97
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Abstract Consistency and consensus using hesitant fuzzy linguistic preference relations (HFLPRs) are two closely related issues for group decision making. However, there are still some gaps that need to be addressed: the normalization methods applied in previous research change the initial information, most approaches modify every element of the original HFLPRs, and the consistency level is uncontrolled in the consensus reaching process. In this paper, two optimization methods are proposed: one ...
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#1Qi Yue (Jiangxi University of Finance and Economics)H-Index: 1
#2Lili Zhang (DUT: Dalian University of Technology)H-Index: 1
Abstract Hesitant fuzzy set (HFS), as an extension of fuzzy set, is deemed as a very useful mean to exhibit hesitant information in handling real-life problems. To enlarge the range of applicability, this paper combines HFS with two-sided matching (TsM). Firstly, this paper retrospects the definitions of hesitant fuzzy Numbers (HFNs) and TsMs, where a new score function of HFN is provided. After that, the TsM decision problem based on HFNs is demonstrated. To solve it, a TsM decision model on th...
1 CitationsSource
#1José Carlos R. Alcantud (University of Salamanca)H-Index: 19
#2Azadeh Zahedi Khameneh (UPM: Universiti Putra Malaysia)H-Index: 5
Last. Adem Kilicman (UPM: Universiti Putra Malaysia)H-Index: 23
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Abstract We propose the first method for aggregating infinite sequences of intuitionistic fuzzy sets in the literature. This new tool allows us to aggregate an infinite list of intuitionistic fuzzy sets over time –a particular case of temporal intuitionistic fuzzy sets– into a traditional intuitionistic fuzzy set. As an application, we define scores and accuracy degrees of temporal intuitionistic fuzzy elements. Then we use these tools to solve the decision making problem where data come in the ...
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#1Chuan Yue (GDOU: Guangdong Ocean University)H-Index: 1
Abstract An extended VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) method in group decision-making (GDM) setting is developed in this paper. The decision information is characterized by picture fuzzy number. A new GDM model is established and applied to software reliability assessment. First, this research finds that the current projection measure is not always reasonable in picture fuzzy setting. To solve this problem, a new normalization projection measure is developed in pictur...
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#1Yaya Liu (USST: University of Shanghai for Science and Technology)H-Index: 4
#2José Carlos R. Alcantud (University of Salamanca)H-Index: 19
Last. Luis Martínez (University of Jaén)H-Index: 46
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A novel hybrid soft set model called intertemporal hesitant fuzzy soft set is proposed, and then, it is showed how it can deal with group decision making problems. This model can be used to incorporate hesitant information that varies across time, when the alternatives are described by their degree of agreement with various characteristics. According to the period of time (whether it is indefinitely long or with a known termination date), the proposed model is, respectively, called long-term and...
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#1Kholood Mohammad Alsager (Qassim University)H-Index: 1
#2N. O. AlshehriH-Index: 10
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