Abstract
A sophisticated three-way decision model utilizing a multi-granularity probabilistic hesitant fuzzy rough set is introduced to mitigate the issue of information loss arising from hesitant fuzzy sets when characterizing decision information. Initially, the properties of probabilistic hesitant fuzzy sets are examined, subsequently proposing a distance measure and loss function tailored to these sets. Following this, a multi-attribute group decision-making model incorporating probabilistic hesitant fuzzy information is established, and pertinent decision rules that satisfy minimal risk criteria are presented. Building on this foundation, a series of critical steps for resolving a category of multi-attribute group decision-making problems that involve probabilistic hesitant fuzzy information is proposed. Lastly, the multi-attribute group decision-making model with probabilistic hesitant fuzzy information is applied to the supervision of urban shared parking platforms. The results indicate that the decision-making process based on probabilistic hesitant fuzzy sets is more reliable, and the decision-making outcome aligns with the actual situation, thus providing valuable decision-making references for managers.
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