Algebraic properties and operator analysis of penta-partitioned intuitionistic neutrosophic soft sets for pattern recognition applications
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Keywords:
penta-partitioned neutrosophic soft set; intuitionistic neutrosophic logic; algebraic operators; parametric transformations; multi-criteria decision-makingAbstract
Complex decision-making problems are uncertain, contradictory and partially ignorant conditions that surpass the representational limits of traditional fuzzy, intuitionistic and neutrosophic soft set models. To overcome these limitations, this paper introduces the penta partitioned intuitionistic neutrosophic soft set (PPINSS), a five component extension that distinctly represents truth, indeterminacy, contradiction, falsity and ignorance. Unlike previous models, PPINSS incorporates an intuitionistic dependency between truth and falsity through the balance relation p =1 -t -f , ensuring a coherent and bounded characterization of uncertainty. Fundamental set-theoretic operations such as complement, subset and equality are formally defined and their algebraic properties are rigorously established. Moreover, a comprehensive family of operators—including necessity () and possibility () transformations, aggregation operators (Å,) and parametric mappings m n m n D , F , ( , ) is introduced to model dynamic uncertainty and interdependent reasoning. These operators are shown to satisfy algebraic consistency, duality and closure within the PPINSS domain. By integrating the intuitionistic interdependence of truth and falsity with a fifth component representing latent ignorance, PPINSS offers a unified, logically coherent and semantically rich framework for modeling complex real-world uncertainties. It serves as an effective analytical foundation for multi-criteria decision analysis, distributed intelligence and cognitive reasoning systems.
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