Operations on Pythagorean Neutrosophic Hypersoft Matrices with TOPSIS Method and their Application in Diagnosing Preterm Births

Abstract

Introduction: Advanced mathematical models that can handle inaccurate and incomplete information are necessary for making decisions in uncertain circumstances. Pythagorean neutrosophic hypersoft matrices offer an adaptable structure for expressing uncertainty in multi-criteria issues. This research presents various operations on these matrices, demonstrates their essential characteristics through proofs, and utilizes them in medical decision-making by employing the max-min average composition and TOPSIS method to diagnose and rank preterm newborn patients.

Objectives: This research seeks to explore the operations and essential characteristics of Pythagorean neutrosophic hypersoft matrices (PNHSMs) and establish a strong decision-making model utilizing max–min average composition and the TOPSIS approach for assessing preterm infant conditions and prioritizing urgent cases.

Methods: A new multi-criteria decision-making method derived from max–min average composition has been introduced. Additionally, an evaluation matrix combined with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was created to evaluate the health status of preterm infants and prioritize patients based on their severity. A numerical example was provided to illustrate the real-world application of the suggested approach.

Results: The suggested framework effectively defined the theoretical characteristics of Pythagorean neutrosophic hypersoft matrices and showed their use in intricate decision-making issues. The combined max–min average composition and TOPSIS method efficiently assessed and prioritized preterm infants, facilitating precise recognition of the most urgent cases. The numerical example validated the effectiveness and practicality of the suggested algorithm.

Conclusions: This study presented operations on Pythagorean neutrosophic hypersoft matrices and demonstrated their characteristics. It additionally suggested a novel decision-making approach utilizing max-min average composition and TOPSIS. The findings indicated that the approach can accurately identify and prioritize critical preterm infants and may assist in decision-making under uncertainty.