Neutrosophic Appurtenance-Inclusion Algebra: A Novel Framework for Personalized Product Design Schemes Decision Modeling

This paper introduces a novel mathematical framework called Neutrosophic Appurtenance-Inclusion Algebra (N-AIA). It extends classical and fuzzy algebraic systems by integrating two distinct relational concepts—appurtenance and inclusion— within a neutrosophic logic environment. Each element in the proposed algebra is described by two neutrosophic triplets, capturing degrees of truth, indeterminacy, and falsehood for both appurtenance and inclusion independently. This dual structure enables more nuanced modeling of ambiguous or uncertain relations between objects and decision criteria. To demonstrate the practical relevance of the proposed framework, we apply N-AIA to the problem of selecting personalized product design schemes. In such settings, customer preferences often involve incomplete, conflicting, or imprecise information. The N-AIA model allows for structured evaluation of design options using neutrosophic measures across both suitability and availability dimensions. The paper defines formal operations, algebraic laws, and comparison rules for N-AIA, and presents multiple realistic examples with full mathematical computations. Results show that the model accurately handles multi-dimensional uncertainty and supports more informed, flexible decision-making. This approach can be extended to other domains where humancentered design and uncertain relationships are critical.

Abstract licence: CC BY-NC

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