Cubic Spherical Neutrosophic Weighted Geometric  Heronian Mean Operator for MCDM with Application to  Fertilizer Selection

S. Gomathi; A. Kalamani; L. Senthil Kumar; Rahul Shukla

Authors

S. Gomathi Department of Mathematics, Rathinam Technical Campus, Coimbatore, India;
A. Kalamani Department of Mathematics, Karpagam College of Engineering, Coimbatore, India;
L. Senthil Kumar Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi, India;
Rahul Shukla Department of Mathematical Sciences & Computing, Walter Sisulu University, Mthatha Campus, South Africa.

Keywords:

Neutrosophic set; Superhypersoft set; Cubic spherical neutrosophic set; Heronian Mean; MCDM.

Abstract

This paper introduces the Cubic Spherical Neutrosophic Weighted Geometric Heronian
Mean (CSNWGHM) operator to aggregating the Cubic Spherical Neutrosophic Set (CSNS) values.
The fundamental properties of idempotency, monotonicity and boundedness are rigorously verified
for this operator. This aggregation operator is designed to effectively handle uncertain or imprecise
information, incorporating a radius parameter for enhanced flexibility. To demonstrate the practical
application, this operator is integrated into Multi - Criteria Decision-Making (MCDM) methods. The
Step – Wise Weight Assessment Ratio Analysis (SWARA) method is employed to calculate the
weights of the criteria. Subsequently, the proposed aggregation operator, in conjunction with a score
function is utilized to identify the best and worst alternatives. An illustrative example showcases the
efficacy in selecting the most appropriate fertilizer for guava and banana trees, using propositions
derived from Neutrosophic SuperHyperSoft Sets (NSHSSs). Furthermore, a sensitivity and
comparative analysis is conducted to establish the stability of this approach and determine the perfect
correlation factor by evaluating various parameter values.

DOI: 10.5281/zenodo.17088758