**6. Conclusions**

This paper presents a new extension to MM operator in the IVPHFS context. Some interesting properties and theorems are also discussed for arriving better theoretical perspective in the field of aggregation and information fusion. The weights of the attributes are also calculated using newly proposed mathematical programming model which uses the DMs' partial information effectively. The data structure used for preference elicitation is a generalization of PHFS concept that mitigates the

problem of assigning a precise occurrence probability to each HFE by allowing interval values as occurrence probability for each HFE. The MM operator has the ability to capture interrelationship between multiple attributes and provides a generalized focus on the aggregation of preferences. The customizable parameter in MM operator allows DMs to clearly understand the effect of risk appetite value on the prioritization order. The idea of extending the MM operator to IVPHFS context and the proposing of a new programming model for attribute weight calculation enriches the data structure for better MAGDM. Some desirable properties of the proposed IVPHFMM operator have analyzed for better understanding the operator and applying the same for MAGDM. From the sensitivity analysis of risk appetite values, we can infer that as values increase, the rank values also increase for each renewable energy source, thus allowing rational prioritization of renewable energy sources. Also, sensitivity analysis is carried out for attribute weight values and they infer that the prioritization order is unchanged and the proposed prioritization procedure is stable even after adequate changes are made to the attributes' weights.

As a part of the future direction, plans are made to extend different generalized operators in the IVPHFS context with a discussion on different Archimedean T-norms and T-conorms. Further, plans are made to propose a new decision framework in the IVPHFS context for better MAGDM and large scale group decision-making.

**Author Contributions:** The individual contribution and responsibilities of the authors were as follows: Author(s) R.K. and M.I.A. designed the research model, collected, pre-processed, analysed the data and the obtained results. They worked on the development of the paper. Authors K.S.R., S.K. and X.P. provided valuable advice throughout the research by sharing insights on model design, methodology and inferences. They also refined the manuscript by providing a valuable suggestion. All the authors have read and approved the final manuscript.

**Funding:** This research was funded by the University Grants Commission (UGC), India and Department of Science & Technology (DST), India under gran<sup>t</sup> number F./2015-17/RGNF-2015-17-TAM-83 and SR/FST/ETI-349/2013.

**Acknowledgments:** Author(s) thank the editors and the anonymous reviewers for their insightful comments which improved the quality of the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
