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• W4313531422 abstract "The probabilistic hesitant fuzzy sets (PHFSs), which have received a lot of attention and have been widely used in many domains, are effective in describing hesitant evaluations. Despite significant progress, entropy and cross-entropy, as the famous uncertainty measures of probabilistic hesitant fuzzy information, have not yet been thoroughly investigated. However, these uncertainty measures are quite important and useful in the context of multi-attribute decision-making (MADM). In this contribution, we revisit the concept of uncertainty measures for probabilistic hesitant fuzzy information by comprehensively considering their fuzziness and hesitancy, and proposed some novel entropy and cross-entropy measures for them. Specifically, the hybrid entropy measures are designed as convex combinations of the fuzzy entropy factor and the hesitant entropy factor, and in the same line of thought, the hybrid cross-entropy measures are also designed as convex combinations of the fuzzy cross-entropy factor and the hesitant cross-entropy factor. It is shown that the hybrid entropy measures are simple in structure, clear in physical meaning, and strong in discriminating capability, while the hybrid cross-entropy measures can avoid the design flaws of existing cross-entropy measures and employ natural symmetry. It is further shown that the hybrid entropy and cross-entropy measures can be designed in pairs and are mutually supportive, which suggests that they are internally unified as the uncertainty measures of probabilistic hesitant fuzzy information. In the end, based on the proposed uncertainty measures, an MADM model is developed within the TOPSIS framework to evaluate a company’s strategic initiatives under probabilistic hesitant fuzzy environment. Numerical results show that these uncertainty measures can support group decision-making effectively and efficiently with probabilistic hesitant fuzzy information." @default.
• W4313531422 created "2023-01-06" @default.
• W4313531422 creator A5082063467 @default.
• W4313531422 date "2023-05-01" @default.
• W4313531422 modified "2023-10-16" @default.
• W4313531422 title "Some uncertainty measures for probabilistic hesitant fuzzy information" @default.
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• W4313531422 doi "https://doi.org/10.1016/j.ins.2022.12.101" @default.
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