Comparisons of probabilistic linguistic term sets for multi-criteria decision making

Bai, Chengzu; Ren, Zhaohui; Qian, Longxia; Wu, Yaning

doi:10.1016/j.knosys.2016.12.020

Cited by 179 publications

(97 citation statements)

References 36 publications

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“…He et al [32] extended the PHFSs to the probabilistic interval preference ordering sets and Hao et al [33] extended it to the probabilistic dual hesitant fuzzy sets. In addition, PHFSs have been extended to probabilistic linguistic term sets [11,34,35]. Although the concept of PHFSs has been extended to various kinds of fuzzy environments and some decision-making methods have been proposed.…”

Section: E(x−e(x))(y−e(y))mentioning

confidence: 99%

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Wang

2017

Symmetry

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Abstract:Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information.

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Section: E(x−e(x))(y−e(y))mentioning

confidence: 99%

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Wang

2017

Symmetry

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“…The PLTSs had been investigated from different viewpoints. Bai et al 2 introduced a new comparison method for the PLTSs. Gou and Xu 7 proposed some novel operational laws for the linguistic terms, the HFLTSs and the PLTSs.…”

Section: Introductionmentioning

confidence: 99%

“…New entropy measures should be developed since the probability information in the PLTSs cannot be omitted. Let us consider two PLTSs: L(P) (1) = {s 1 (0.5), s 2 (0.5)} and L(P) (2) = {s 1 (0.01), s 2 (0.99)} based on a linguistic term set S = {s 0 , . .…”

Section: Introductionmentioning

confidence: 99%

Entropy Measures of Probabilistic Linguistic Term Sets

Liu¹,

Jiang²,

Zhang³

2018

IJCIS

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The probabilistic linguistic term sets (PLTSs) are powerful to deal with the hesitant linguistic situation in which each provided linguistic term has a probability. The PLTSs contain uncertainties caused by the linguistic terms and their probability information. In order to measure such uncertainties, three entropy measures are proposed: the fuzzy entropy, the hesitant entropy, and the total entropy. The fuzzy entropy measures the fuzziness of the PLTSs, and the hesitant entropy measures the hesitation of the PLTSs. To facilitate the computation of all uncertainties contained in the PLTSs, the total entropy is proposed. Some properties and some formulas of the entropy measures are introduced. A multi-criteria decision making model based on the PLTSs is introduced by using the proposed entropy measures. An illustrative example is provided and the comparison analysis with the existing method is given.

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“…This theory proposed by Pang et al [6] plays a key role in the decision process where experts express their preferences [7][8][9]. Nowadays, PLTSs have become a hot topic in the area of hesitant fuzzy linguistic term sets (HFLTSs) [10][11][12] and hesitant fuzzy sets (HFSs) [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Bai et al [7] stated that the existing approaches associated with PLTSs are limited or highly complex in real applications. Thus they established more appropriate comparison method and developed a more efficient way to handle PLTSs.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making

Agbodah

Liang

2017

Symmetry

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Abstract:As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances.

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Comparisons of probabilistic linguistic term sets for multi-criteria decision making

Cited by 179 publications

References 36 publications

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Entropy Measures of Probabilistic Linguistic Term Sets

Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making

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