Bonferroni Mean Operators on Weighted Hesitant Fuzzy Set and Its Application in Multi-Criteria Symmetric Group Decision Making

The Bonferroni mean operator, as a powerful aggregation operator, is widely applied as a solution to various problems, owing to its strong ability to capture relevance between different variables. Compared with other extensions, the weighted hesitant fuzzy set (WHFS) can depict the fuzziness of relationships between things better. Considering the advantage of weighted hesitant fuzzy sets (describing fuzziness more objectively in real problems), the Bonferroni mean is introduced into weighted hesitant fuzzy set theory. In this paper, by merging and transforming weighted hesitant fuzzy weighted average/geometric (WHFWA/WHFWG) operators, a novel weighted hesitant fuzzy geometric Bonferroni mean (WHFGBM) operator is developed using weighted hesitant fuzzy theory, so as to fuse information and provide idea support for practical tasks under various experts’ common judgment. To show the effectiveness of the novel operator intuitively, the comparison results of symmetric numeric examples are displayed.