Entropy Measures of Probabilistic Linguistic Term Sets

The probabilistic linguistic term sets (PLTSs) are powerful to deal with the hesitant linguistic situation in which each provided linguistic term has a probability. The PLTSs contain uncertainties caused by the linguistic terms and their probability information. In order to measure such uncertainties, three entropy measures are proposed: the fuzzy entropy, the hesitant entropy, and the total entropy. The fuzzy entropy measures the fuzziness of the PLTSs, and the hesitant entropy measures the hesitation of the PLTSs. To facilitate the computation of all uncertainties contained in the PLTSs, the total entropy is proposed. Some properties and some formulas of the entropy measures are introduced. A multi-criteria decision making model based on the PLTSs is introduced by using the proposed entropy measures. An illustrative example is provided and the comparison analysis with the existing method is given.

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