A cosine similarity measures between hesitancy fuzzy graphs and its application to decision making

A new cosine similarity measure between hesitancy fuzzy graphs, which have been shown to have greater discriminating capacity than certain current ones in group decision making problems by example verification. This study proposes a novel method for estimating expert-certified repute scores by determining the ambiguous information of hesitancy fuzzy preference relations as well as the regular cosine similarity grades from one separable hesitancy fuzzy preference relation to some others. The new approach considers both "objective" and "subjective" information given by experts. We construct working procedures for assessing the eligible reputational scores of the experts by applying hesitancy fuzzy preference relations. In an evaluation in which multiple conflicting factors are taken into consideration, this can be applied to increase or reduce the relevancy of specified criteria. Applying the two effective methods, the newly developed cosine similarity measure, the energy of hesitancy fuzzy graph, and we provide a solution to a decisional issue. Finally, the two working procedures and examples are given to verify the practicality and dominance of the proposed techniques.