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On Optimal Priority Modelling of Group Intuitionistic Fuzzy Preference Relations with Normal Uncertainty Distribution

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Abstract

The uncertainty distribution can more effectively express the uncertainty of decision makers’ judgments during a pairwise comparison of any alternatives. This paper investigates the priority models of group intuitionistic fuzzy preference relations with normal uncertainty distribution. The mathematical equivalence between the membership, non-membership degree interval fuzzy preference relation and the intuitionistic fuzzy preference relation is constructed, showing that there exists an inverse relationship between the priority of alternatives using these two types of interval preference relations. The new optimal models regarded the event that the deviation between the ideal judgement meeting the multiplicative consistency and the actual judgement obeying normal uncertainty distribution shall not exceed a threshold value under the given belief degree as a constraint, and regarded the minimum sum of all the threshold values as the objective function. The chance constraint was introduced to measure the degree to which multiplicative consistency can be realized under different belief degrees. The priority model provides a new method for simulating uncertainty and fuzziness in the real-world decision making environment.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 71571104 and 71171115, a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Natural Science Foundation of Jiangsu, China under Grant No. BK20141481, and the fifth issue of the “333 Project” funded research project under Grant No. BRA2017456.

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  1. College of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Lihong Wang & Zaiwu Gong

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  1. Lihong Wang
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  2. Zaiwu Gong
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Correspondence to Zaiwu Gong.

Additional information

Lihong Wang is a PhD candidate of College of Management Science and Engineering, School of Applied Meteorology, Nanjing University of Information Science and Technology. Her areas that are interested in include group decision-making and sustainable development.

Zaiwu Gong is a professor of College of Management Science and Engineering, Nanjing University of Information Science and Technology. His areas that are interested in include group decision-making, systems engineering supporting, and risk analysis.

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Wang, L., Gong, Z. On Optimal Priority Modelling of Group Intuitionistic Fuzzy Preference Relations with Normal Uncertainty Distribution. J. Syst. Sci. Syst. Eng. 28, 510–525 (2019). https://doi.org/10.1007/s11518-019-5425-9

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