Bipolar Neutrosophic Dombi-Based Heronian Mean Operators and Their Application in Multi-criteria Decision-Making Problems

Abstract Dombi operations based on the Dombi t-norm (TN) and t-conorm (TCN) have the advantage in terms of operational parameter flexibility in dealing with varying degrees of uncertainty and aggregation requirements. Meanwhile, Heronian mean (HM) operator is an effective technique for capturing the interrelationship between any number of inputs. Bipolar neutrosophic set (BNS) offers the ability to represent both positive and negative information as well as indeterminate information. It is beneficial in cases where there is uncertainty or insufficient information. However, the existing Dombi operator under BNS do not take into account the interrelationship between input arguments. To overcome this limitation, this study incorporates Dombi operator into HM and propose the bipolar neutrosophic Dombi Heronian mean aggregation operator. This paper introduces two type of aggregation operators namely bipolar neutrosophic Dombi-based generalized weighted Heronian mean (BND-GWHM), and bipolar neutrosophic Dombi-based improved generalized weighted Heronian mean (BND-IGWHM). The proposed operators are integrated into MCDM procedure. The influence of different parameter values on decision-making results is discussed. Finally, a comparison analysis with existing methods is also provided.