An assessment of fertilizer spraying drones based on hesitancy fuzzy similarity measures for sustainable green development

Abstract

This research proposes a new similarity measure on hesitancy fuzzy graphs. The similarity measures are crucial concepts to explore the closeness between fuzzy graphs. The available imprecise and inconsistent data were more effectively handled by fuzzy similarity measures and intuitionistic fuzzy similarity measures. With time in decision-making theory, a complex frame of the background that occurs cannot be specified entirely by these fuzzy graphs but generalized fuzzy graphs like the hesitancy fuzzy graph can handle such a situation efficiently. The applicability of Hesitancy Fuzzy Graph (HFG) attracted the researchers to generalize ranking order based on the working procedures I, II of Xu’s approach and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. For this purpose, we first define hesitancy fuzzy preference relations, Laplacian energy, and similarity measures in these HFG. The decision-making technique is then proposed in which a weighting technique is developed by building an optimal model based on the proposed Laplacian energy and similarity measure under a hesitancy fuzzy environment. This research studies the decision-making problem in which the preference information given by the experts takes the form of Hesitancy Fuzzy Preference Relations (HFPRs) and the information about experts’ weights are completely unknown. This research utilizes the hesitancy fuzzy weighted averaging operator to aggregate all individual HFPRs into a collective HFPR. Then, based on the degree of similarity between the individual HFPRs and the collective ones, we develop an approach to determine the experts’ weights. Moreover, based on HFPRs, in which the similarity measures between the collective preference relation and hesitancy fuzzy ideal solution are used to rank the given alternatives. We provide an illustrative numerical example to illustrate the mentioned approach and also we compare the aggregate results of the two techniques.