提出多层模糊逻辑框架,解决决策中矛盾信息的融合问题。
Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
- 用犹豫与矛盾控制的凸聚合机制建模中介算子
- 构建连续双格结构表示真值与假值独立对
- 适用于传感器融合等安全关键场景的透明决策
中介模糊逻辑最初旨在调和模糊控制与决策中的犹豫或冲突评估,但其逻辑与语义基础在类型1之外仍不完善。本文构建了类型1核心及区间型2、粒度型3与量子扩展的统一框架。将中介算子定义为由犹豫与矛盾控制的凸聚合,将中介真值建模为连续双格结构中的独立真-假对,并在标准t-范数模糊逻辑基础上引入中介联结词。证明了无中介公式的保真性、对偶一致性与保守性。形式化了区间型2真值、粒度索引局部评估以及希尔伯特空间上的效应与密度算子的语义扩展。通过自主制动传感器融合实例,展示了该框架如何在不完备、异构且轻微矛盾证据下支持透明、保守、以安全为先的决策。在合理假设下,高阶形式可退化至类型1情形,揭示了多层级间的一致性,为智能决策系统未来研究提供可靠支撑。
原文摘要 · Abstract (English)
Mediative Fuzzy Logic was conceived as a practical scheme for reconciling hesitant or conflicting assessments in fuzzy control and decision-making. However, its logical and semantic foundations remain underdeveloped, especially beyond operational type-1 settings. This article develops a unified account of the type-1 core together with interval type-2, granular type-3, and quantum extensions. We characterize the mediative operator as a convex aggregation controlled by hesitation and contradiction, model mediative truth values as independent truth-falsity pairs in a continuous bilattice-like structure, and introduce a propositional system extending a standard t-norm-based fuzzy logic with a mediative connective. We establish soundness, paraconsistency, and conservativity over the underlying fuzzy base for formulas without mediation, and formulate coherent semantic extensions to interval type-2 truth values, granule-indexed local evaluations, and effects and density operators on Hilbert spaces. An autonomous-braking sensor-fusion example illustrates how the framework supports transparent, conservative, and safety-first decisions under incomplete, heterogeneous, and mildly contradictory evidence. Under suitable assumptions, the higher-level formulations reduce to the type-1 case, clarifying coherence across levels and reliably supporting future work in intelligent decision systems.
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