A Framework of Near-Intuitionistic Fuzzy Soft Sets with Applications to Uncertainty-Based Diagnosis

This paper introduces a novel near-intuitionistic fuzzy soft (NIFS) framework that unifies nearness approximation and intuitionistic fuzzy soft set theory to address uncertainty characterized by both local similarity and indeterminacy. Within this framework, fundamental operations and inclusion relations on NIFS sets are rigorously defined, and their essential algebraic properties are systematically derived, establishing a coherent mathematical foundation. Building on the proposed theory, two NIFS-based multi-criteria decision-making procedures are developed that explicitly exploit lower and upper near approximations, along with intuitionistic fuzzy evaluations. The applicability of the framework is demonstrated through medical diagnosis problems, where vague symptom descriptions and incomplete information are inherent. Experimental results show that the proposed NIFS-based procedures provide effective and interpretable decision support while maintaining theoretical rigor. Overall, the study advances the mathematical development of fuzzy soft set models and highlights the potential of the NIFS framework for intelligent decision-support systems in complex and uncertain environments.