Core Concepts Behind Quadripartitioned Neutrosophic Soft Block Matrices

Abstract

We introduce quadripartitioned neutrosophic soft block matrices, extending neutrosophic soft 
matrices with a four-part structure to model uncertainty, indeterminacy, falsity, and a new 
component: uncertainty, in decision-making. This enhancement overcomes limitations of 
traditional neutrosophic soft matrices by comprehensively representing complex situations where 
all four aspects must be simultaneously considered. Each matrix element is divided into four sub
components for a more nuanced analysis of the decision alternatives and criteria. The paper details 
fundamental matrix operations (addition, subtraction, multiplication, and inversion) and explores 
their properties. Case studies in decision support systems and optimization problems illustrate the 
framework's applicability, particularly where traditional methods are insufficient. The model 
proves especially valuable for complex decision-making in artificial intelligence, pattern 
recognition, and fuzzy logic, handling multiple uncertainty layers. Finally, we examine the 
theoretical basis and practical uses of quadripartitioned neutrosophic soft block matrices, 
providing a new tool for soft computing and decision science.

DOI: 10.5281/zenodo.15749784