Abstract
Heronian mean (HM) operators are powerful aggregation operators that consider the interrelationship of two input arguments. HM operators have been utilized to solve many multi-criteria decision-making (MCDM) problems under different environments. However, the existing HM does not take into consideration the overall interaction of input arguments. Therefore, to address this issue, the Shapley fuzzy measure (SFM) is combined with an improved generalized weighted HM (IGWHM) operator under an interval neutrosophic vague set (INVS). The INVS is structured into several membership degrees appropriate for dealing with incomplete and inconsistent information as well as reducing the information loss during the decision elicitations. This paper introduces two aggregation operators: interval neutrosophic vague Shapley improved generalized weighted HM (INVSIGWHM) and interval neutrosophic vague Shapley improved generalized geometric-weighted HM (INVSIGGWHM). Then, the three essential algebraic properties of the proposed aggregation operators are also discussed for both operators. Furthermore, based on the proposed INVSIGWHM and INVSIGGWHM operators, we suggest two multi-criteria decision-making methods in which information is given in interval neutrosophic vague. A numerical example of investment decision is presented to illustrate the effectiveness of developed methods. It is found that the car company is the best alternative among the others. Besides, sensitivity analysis using two existing parameters is performed on the proposed method to demonstrate the effect of ranking order on alternatives. From this analysis, it can be seen that the parameter p,q significantly influences the aggregation results. Finally, a comparative analysis is presented in two approaches: to validate the proposed method and to demonstrate the advantages. The comparative analysis shows that the proposed method is reliable and practical in solving decision-making problems involving the total interaction of decision-makers and criteria weights. The suggested decision-making framework under INVS has effectively handled the overall criteria interactions. In future, the proposed method can be integrated with other neutrosophic sets.