Nonagonal Neutrosophic Number: Analytical Aspects and its  Role in Optimization technique for transportation problem

Sincy B; Riya V M

Authors

Sincy B Department of Mathematics, Sree Narayana College Chengannur, St. Joseph’s College Irinjalakuda, University of Calicut, Kerala 680712, India;
Riya V M Department of Mathematics, Sree Narayana College Nattika, University of Calicut, Kerala 680566, India;

Keywords:

Transportation problem, Nonagonal neutrosophic numbers, Defuzzification, Crisp data, Optimization

Abstract

Neutrosophic numbers have received increasing attention from researchers and
industrialists to address the indeterminacy and uncertainty inherent in real-life decision-making.
This study aims to solve the transportation problem where supply, demand and transportation costs
are Nonagonal Neutrosophic Numbers (NNNs). In the existing literature, various methods have
been introduced to solve transportation problems (TPs) involving neutrosophic parameters. The
application of Nonagonal Neutrosophic Numbers to transportation problems is a relatively recent
development. NNNs offer a more detailed and adaptable representation of uncertainty by utilizing a
nine-parameter structure that captures the degrees of truth, indeterminacy, and falsity. Therefore, in
this paper, we solve the transportation problem using Nonagonal Neutrosophic Numbers for the
first time. To facilitate this, we introduce two novel score functions for converting NNNs into crisp
values. Based on these, we propose an algorithmic framework to obtain the optimal solution
effectively. To exemplify the effectiveness of the proposed method, we solved a numerical example,
and the obtained results are presented and compared with those in the existing literature. Finally,
the significance of this study and potential directions for future research are mentioned.

DOI 10.5281/zenodo.18262716