Multi-Valued Interval Neutrosophic Soft Sets and Their  Aggregation Operators

Nor Liyana Amalini Mohd Kamal; Lazim Abdullah; Ilyani Abdullah; Vakkas Uluçay; Khalid Naeem

Authors

Nor Liyana Amalini Mohd Kamal College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Negeri Sembilan Branch, Rembau Campus, 71300 Rembau, Negeri Sembilan, Malaysia;
Lazim Abdullah Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia;
Ilyani Abdullah Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia;
Vakkas Uluçay Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey;
Khalid Naeem Department of Mathematics & Statistics, University of Lahore, Pakistan;

Keywords:

arithmetic aggregation; geometric aggregation; multi-valued neutrosophic set; soft set; decision-making

Abstract

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.

DOI 10.5281/zenodo.17662136