An innovative quantum–fuzzy paradigm for time- and context-sensitive membership: Quantive logic

Abstract

Uncertainty in real-world decision problems is rarely static or one-dimensional: the relevance of evidence changes over time, depends on context, and is shaped by interactions between multiple criteria. Classical fuzzy logic provides a flexible scalar notion of membership, but it typically treats each criterion in isolation and does not natively encode temporal or contextual dynamics. Quantum-inspired models, on the other hand, offer rich Hilbert-space representations but are often difficult to integrate with everyday decision-making tasks. This paper proposes Quantive Logic (QL), a quantum-inspired fuzzy framework for time- and context-sensitive membership. In QL, each element is assigned a quantive membership state, represented as a vector in a complex Hilbert space. Conventional fuzzy degrees are recovered as suitable projections of this state, while phase and superposition capture interactions and context effects between criteria. We formalize how quantive membership states are initialized from classical information and updated through linear operators that model temporal evolution and contextual shifts. To illustrate the framework, we outline a multi-criteria credit-risk assessment scenario in which applicant profiles are encoded as quantive membership states and updated under changing economic conditions. This example shows how QL can refine risk judgments when interactions between criteria and scenario-dependent effects are important. Rather than competing with existing fuzzy or probabilistic models, QL is intended as a complementary layer that enriches membership representation wherever time, context, and interaction effects cannot be ignored.