A Neutrosophic Approach for Evaluating the Multimedia-Aided College Piano  Instruction Evaluation Techniques: Dombi-Based Heronian Mean Operators

Lan Yao

Authors

Lan Yao College of Music and Dance, Hunan University of Arts and Science, Changde, Hunan, 415000, China

Keywords:

Neutrosophic Sets (NS), Single-Valued Neutrosophic Sets (SVNS), Interval Valued Neutrosophic Sets (IVNS), Neutrosophic Aggregation Operators, Dombi Neutrosophic Operators, Neutrosophic Ranking Method

Abstract

This paper contributes to the body of neutrosophic knowledge through
proposing an advanced neutrosophic aggregation paradigm through the development of
the Cubic Bipolar Neutrosophic Soft Set (CBNSS) aggregation operator based on the
combination of Dombi operation as well as Weighted Heronian Mean. It is named CBNS
D-GWHM. CBNSS is formally defined to extend the expressive capacity of neutrosophic
science by integrating the cubic and bipolar structures within soft set theory to enable
simultaneous modeling of interval-valued, precise, positive, and negative membership
information. With established theoretical properties, our CBNS-D-GWHM operator can
provide a highly flexible and parameterized aggregation mechanism, capable of capturing
complex scenarios. An illustrative case study in the domain of multimedia-aided college
piano instruction demonstrated the applicability and robustness of CBNS-D-GWHM,
which highlighted its capacity to synthesize nuanced expert knowledge. The findings not
only advance the state of neutrosophic aggregation theory but also provide a novel
foundation for further extensions in complex decision modeling and information fusion
tasks.

DOI: 10.5281/zenodo.16730056