Prioritization of Geothermal Energy Systems for Industrial Applications by Using Hesitant Bipolar Fuzzy Multi-Criteria Decision-Making Technique Based on Dombi Operators (Contemporary Mathematics, 2025)
The proposed research fills a significant gap in the decision-making technique for evaluating geothermal energy systems in industrial processes by introducing a new approach involving Hesitant Bipolar Fuzzy (HBF) Sets (HBFSs) with Dombi operators. The existing literature has mostly focused on uncertainty only, overlooking the aspect that decisions tend to be imprecise, bipolar, and hesitant in reality. To overcome this gap, we first introduce Dombi operators in the context of HBFSs, thereby improving the parametric flexibility in handling more complex uncertain information. Based on these operators, we establish an HBF Multi-Criteria Decision-Making (MCDM) method for the ranking of geothermal energy systems. The applicability of our proposed methodology for prioritizing different types of geothermal energy systems for industrial applications is illustrated in a detailed case study that supports the theoretical framework. The benefit of the suggested method is also supplemented by the comparison of the proposed method with the previous methods and evidence of the capability to handle uncertainty and make more precise and confident decisions. This study offers an important theoretical as well as practical contribution to decision-making practices and the choice of sustainable energy systems for geothermal energy options under uncertainty, offering decision-makers a robust framework of analysis. Moreover, we have the following key findings or outcomes of proposed research. • Development of HBF Dombi Weighted Averaging (HBFDWA) operators. • Development of HBF Dombi Ordered Weighted Averaging (HBFDOWA) operators. • Development of HBF Dombi Weighted Geometric (HBFDWG) operators. • Development of HBF Dombi Ordered Weighted Geometric (HBFDOWG) operators. • A case study is performed based on the developed operators to rank geothermal energy systems. • A comparative analysis is performed to show the superiority of the proposed approach. • A sensitivity analysis is discussed to show the influences of the parameter.
Keywords: geothermal energy systems, industry, MCDM technique, hesitant bipolar fuzzy set