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Computers & Industrial Engineering, 2019
Abstract The development of social economy has rendered the decision-making environment more complex. To better adapt to the environment and solve practical decision-making problems, this study uses the probabilistic linguistic terms set (PLTS) to describe qualitative information, which can not only provide every possible evaluation value, but can ...
Peide Liu, Ying Li 0041
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Abstract The development of social economy has rendered the decision-making environment more complex. To better adapt to the environment and solve practical decision-making problems, this study uses the probabilistic linguistic terms set (PLTS) to describe qualitative information, which can not only provide every possible evaluation value, but can ...
Peide Liu, Ying Li 0041
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International Journal of Fuzzy Systems, 2021
In the era of uncertain information everywhere, the Probabilistic Hesitant Fuzzy sets (PHFs), utilizing the possible numbers and its possible membership degrees to descript decision-makers’ behavior, has been brought about widespread attention. Scholars from all over the world applied numerous approaches in this environment since Probabilistic Hesitant
Ningna Liao +2 more
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In the era of uncertain information everywhere, the Probabilistic Hesitant Fuzzy sets (PHFs), utilizing the possible numbers and its possible membership degrees to descript decision-makers’ behavior, has been brought about widespread attention. Scholars from all over the world applied numerous approaches in this environment since Probabilistic Hesitant
Ningna Liao +2 more
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Computers & Industrial Engineering, 2020
Abstract The hesitant fuzzy element (HFE), as an extension of fuzzy numbers, has received much attention and the occurrence probabilities of each membership in the HFEs are assumed to be equal, i.e., the decision makers (DMs) share the same preference for each membership. Anecdotal observations suggest otherwise.
Wei Liang, Mark Goh, Ying-Ming Wang 0001
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Abstract The hesitant fuzzy element (HFE), as an extension of fuzzy numbers, has received much attention and the occurrence probabilities of each membership in the HFEs are assumed to be equal, i.e., the decision makers (DMs) share the same preference for each membership. Anecdotal observations suggest otherwise.
Wei Liang, Mark Goh, Ying-Ming Wang 0001
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Journal of Intelligent & Fuzzy Systems, 2023
As a decision information preference which includes membership degree (MD), non-membership degree (NMD), and probability, the probabilistic dual hesitant fuzzy set (PDHFS) is a crucial tool for effectively expressing uncertain information. In the domains of multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM ...
Pingping Wang, Jiahua Chen
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As a decision information preference which includes membership degree (MD), non-membership degree (NMD), and probability, the probabilistic dual hesitant fuzzy set (PDHFS) is a crucial tool for effectively expressing uncertain information. In the domains of multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM ...
Pingping Wang, Jiahua Chen
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A probabilistic theory of the coincidence method. I. Centrosymmetric space groups
Acta Crystallographica Section A, 1977A theory is given for non-centrosymmetric space groups which permits, for each specially related pair of phases of type (ϕH1 + H2, ϕH1Rp + H2Rq), the calculation of the expected value of a seminvariant cosine. In order to make full use of the symmetry, the mathematical device of the joint probability distribution functions has been suitably combined ...
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Artificial intelligence (AI) technologies selection drives innovation and boosts efficiency across industries. It involves multi-criteria group decision-making (MCGDM) with evaluations from different decision-makers (DMs). Probabilistic uncertain linguistic term sets (PULTSs) help manage uncertainty and provide flexible decision-making.
Shuping Wan +3 more
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Shuping Wan +3 more
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