Abstract
The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application.
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