Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

Zhang, Xu; Zhou, Wei

doi:10.1007/s10700-016-9257-5

Cited by 238 publications

(189 citation statements)

References 23 publications

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“…In order to rank the PHFEs, Xu et al [41] introduced the score function and indeterminacy index function of PHFEs. As a matter of fact, the score function and indeterminacy index function can be regarded as expect mean and variance of PHFEs.…”

Section: Definitionmentioning

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: Definitionmentioning

confidence: 99%

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

Wang

2017

Symmetry

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“…It allows decision makers to give multiple membership values, but has the deficiency to deal with probabilities of preference degrees. To make hesitant fuzzy sets more compatible with real life, Xu and Zhou [35] defined hesitant probabilistic fuzzy element (HPFE) and hesitant probabilistic fuzzy set (HPFS).…”

Section: Preliminariesmentioning

confidence: 99%

“…Algorithms 11-29 will provide the consistent individual HPFPRs and the group HPFPR with agreement among decision makers. To comprehend final standing of the alternatives, first for the alternative the th row of group HPFPR is aggregated by HPFA operator (44) and secondly the aggregated HPFEs are ordered according to their score and deviation [35]. In form of the following algorithm a complete decision model is presented.…”

Section: Decision Support Model For Group Decision Making With Hpfprsmentioning

confidence: 99%

“…They also develop the aggregation operator of this set and proposed the extended TOPSIS version to handle the multicriteria group decision making problems. By getting the motivation from the hesitant fuzzy set and probabilistic linguistic term set, Xu and Zhou proposed the concept of hesitant probabilistic fuzzy set [35]. They investigated several aggregation operators with properties for hesitant probabilistic fuzzy set.…”

Section: Introductionmentioning

confidence: 99%

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Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

Bashir

Rashid

Iqbal

2018

Mathematical Problems in Engineering

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Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

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“…Zhang et al [18] introduced the concept of probabilistic linguistic preference relations to present the DMs preferences. Under the hesitant probabilistic fuzzy environment, Zhou and Xu [19] studied the consensus building with a group of decision makers. PLTSs generalize the existing models of HFLTSs and HFSs so as to contain hesitations and probabilities.…”

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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Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

Cited by 238 publications

References 23 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

Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

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

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