Generalized Dombi Weighted Aggregation Operators for Multi-attribute Decision Making with Hesitant Fuzzy Information

Abstract

Because of two key issues: the presentation of attribute values and the aggregation of available data to form a preference of alternatives, multi-attribute decision making (MADM) is attracting numerous researchers in these days. In contrast to fuzzy set theory, hesitant fuzzy sets (HFSs) are more versatile and comprehensive tools for the representation of attribute values, whereas aggregation operators (AOs) are considered effective tools for the purpose of aggregation in fuzzy set theory. The existence of an aggregation operator (AO) which is capable of providing the necessary generality and versatility in altering perceptions of risk when aggregating attribute data under HFSs has not yet been disclosed. In spite of the fact that weighted AOs were invented earlier in order to attempt to fulfill the above-mentioned scenarios, they are still based on algebraic, Einstein, Hamacher, and Dombi operations. Thus, the primary objective of this study is to construct some comprehensive and adaptable AOs that may be used to address MADM issues with hesitant fuzzy (HF) data. This viewpoint allows us to begin by constructing new operations between HF elements that are based on generalized Dombi (GD) operations. Following that, we construct HF-GD weighted averaging and geometric AOs along with their ordered forms. We will discuss the effectiveness of several of the suggested AOs. Next, we set up a technique for MADM that is based on the HFS operators. Then, we offer an efficient instance involving the selection of an e-commerce Web site to illustrate the suggested method’s decision phases. We undertake a validity check to ensure the authenticity of our recommended AOs. Additionally, we conduct a sensitivity analysis using a variety of attribute weight sets to ascertain the robustness of our recommended methodology. Furthermore, we add a detailed comparative analysis to demonstrate our model’s superiority.