Core Concepts Behind Quadripartitioned Neutrosophic Soft Block Matrices - S. Ramesh Kumar; A. Stanis Arul Mary (Neutrosophic Sets and Systems)
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 subcomponents 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.