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Probabilistic linguistic decision-making based on the hybrid entropy and cross-entropy measures

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Abstract

In fuzzy decision-making, the probabilistic linguistic term sets (PLTSs) are flexible in depicting people’s linguistic evaluations. As the uncertainty measures of PLTSs, entropy and cross-entropy are the important decision-making tools. Generally speaking, the uncertainty of PLTSs can be studied from two facets, which are known as hesitancy and fuzziness. To better reflect these uncertainties, some hybrid entropy and cross-entropy measures of PLTSs are developed in this work. It is shown that the hybrid entropy measures are simple in structure, clear in physical meaning and strong in discriminating ability, while the hybrid cross-entropy measures can avoid the design flaws of existing measures and possess natural symmetry. It is also shown that the hybrid entropy and cross-entropy measures can be designed in pairs, mutually supportive and inherently unified as the uncertainty measures. In the ends, a multi-attribute decision-making (MADM) model, based on these uncertainty measures of PLTSs, is developed within the famous TOPSIS framework to select the best cloud computing platform.

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Acknowledgements

The author is very grateful to the editors and anonymous reviewers for their insightful comments which have led to an improved version of this paper.

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  1. Army Command College of PLA, Nanjing, 210045, China

    Bing Fang

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Correspondence to Bing Fang.

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Fang, B. Probabilistic linguistic decision-making based on the hybrid entropy and cross-entropy measures. Fuzzy Optim Decis Making 22, 415–445 (2023). https://doi.org/10.1007/s10700-022-09398-9

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