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Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

by 1, 2 and 3,*
1
School of Economics and Management, Beihang University, Beijing 100191, China
2
China Institute of Marine Technology and Economy, Beijing 100081, China
3
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1574; https://doi.org/10.3390/math8091574
Received: 8 July 2020 / Revised: 3 September 2020 / Accepted: 10 September 2020 / Published: 12 September 2020
(This article belongs to the Section Fuzzy Set Theory)
The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis. View Full-Text
Keywords: q-rung dual hesitant fuzzy sets; q-rung probabilistic dual hesitant fuzzy sets; power Muirhead mean; multi-attribute decision-making q-rung dual hesitant fuzzy sets; q-rung probabilistic dual hesitant fuzzy sets; power Muirhead mean; multi-attribute decision-making
MDPI and ACS Style

Li, L.; Lei, H.; Wang, J. Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making. Mathematics 2020, 8, 1574. https://doi.org/10.3390/math8091574

AMA Style

Li L, Lei H, Wang J. Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making. Mathematics. 2020; 8(9):1574. https://doi.org/10.3390/math8091574

Chicago/Turabian Style

Li, Li; Lei, Hegong; Wang, Jun. 2020. "Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making" Mathematics 8, no. 9: 1574. https://doi.org/10.3390/math8091574

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