Multi-Valued Interval Neutrosophic Soft Sets and Their Aggregation Operators

Recent studies have increasingly focused on aggregation within the neutrosophic environment due to its capability to handle ambiguity and uncertainty. However, to the authors' information, no current study has investigated aggregation operators for multi-valued interval neutrosophic soft numbers (MVINSSs) in the context of alternative ranking for decision-making problems. This paper proposes two novel aggregation operators: the multi-valued interval neutrosophic soft-weighted geometric averaging (MVINSWGA) and the multi-valued interval neutrosophic soft-weighted arithmetic averaging (MVINSWAA) operators under the MVINSS framework. The fundamental properties of the proposed operators, including idempotency, monotonicity, and boundedness, are established. In addition, a structured multi-criteria group decision-making (MCGDM) procedure incorporating the proposed operators is introduced. A numerical example involving software selection is provided to illustrate the applicability of the suggested approach. Comparative analysis confirms the consistency of ranking results, indicating that the MVINSWGA and MVINSWAA operators are robust and effective in addressing MCGDM problems within the MVINSS environment.