Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
Quick Take
Mediative Fuzzy Logic extends type-1 foundations to type-2, type-3, and quantum frameworks, enhancing decision-making under uncertainty. It introduces a mediative operator for aggregating conflicting assessments, ensuring soundness and paraconsistency, and supports intelligent systems like autonomous braking through its robust semantic structure.
Key Points
- Develops a unified framework integrating type-1, type-2, type-3, and quantum fuzzy logic.
- Mediative operator aggregates conflicting truth values, enhancing decision-making clarity.
- Establishes soundness and paraconsistency for formulas without mediation.
- Supports intelligent systems with examples like autonomous braking under contradictory evidence.
- Clarifies coherence across fuzzy logic levels, aiding future intelligent decision systems.
Article Content
From source RSS / original summaryarXiv:2605. 22900v1 Announce Type: new Abstract: 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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