Application of Neutrosophic SuperHyperSoft Sets in MADM

Ramesh Ramasamy; Krishnaprakash Shanmugavel; Florentin Smarandache

Authors

Ramesh Ramasamy Department of Science and Humanities, Dr. Mahalingam College of Engineering and Technology, Pollachi, Tamilnadu, India - 642 003;
Krishnaprakash Shanmugavel Department of Science and Humanities, Sri Krishna College of Engineering and Technology, Coimbatore, Tamilnadu, India – 641 008;
Florentin Smarandache University of New Mexico, Gallup Campus, United States NM 87301;

Keywords:

Neutrosophic SuperHyperSoft Sets, SuperHyperSoft Sets, Neutrosophic Soft Sets, Neutrosophic Sets.

Abstract

In this work, we introduce the concept of Neutrosophic SuperHyperSoft Sets (NSHSS) by
considering a universe of discourse and disjoint attribute structures, and develop fundamental operations
including addition, multiplication, scalar multiplication, and scalar exponentiation. A novel
Neutrosophic SuperHyperSoft Weighted Aggregation (NSHSWA) operator is proposed, and a new
entropy measure is defined to quantify uncertainty, with its theoretical properties validated. Building on
this, we propose a Multi-Attribute Decision-Making (MADM) framework for selecting optimal mobile
phones by combining NSHSS with entropy-based weighting. Five primary criteria- operational efficiency,
power endurance, imaging capability, cost, and robustness are evaluated using power sets and
neutrosophic modelling to capture uncertainty in user preferences. Subjective linguistic evaluations are
mapped to neutrosophic values, and aggregated using the NSHSWA operator. Among 162 propositions
constructed, the top alternatives are identified and ranked using a neutrosophic score function. The
proposed methodology offers a comprehensive and reliable tool for guiding consumers toward selecting
high quality mobile phones based on personalized needs, while providing a strong foundation for future
uncertain information modelling and decision support.

DOI: 10.5281/zenodo.15314856