Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
This paper systematically develops the core of Mediative Fuzzy Logic and extends it to interval type-2, granular type-3, and quantum versions, establishing a convex aggregation operator controlled by hesitation and contradiction, proving soundness, paraconsistency, and conservativity, and demonstrating its transparent, conservative, and safety-first decision-making capabilities through an autonomous braking sensor fusion example.
Article intelligence
Key points
- Mediative Fuzzy Logic was proposed for reconciling hesitant or conflicting assessments in fuzzy control and decision-making.
- The paper unifies the type-1 core and extends to interval type-2, granular type-3, and quantum extensions.
- The mediative operator is characterized as convex aggregation controlled by hesitation and contradiction, with a propositional system introduced.
- An autonomous braking sensor fusion example illustrates the framework's application in safety-first decisions under incomplete and contradictory evidence.
Why it matters
This matters because mediative Fuzzy Logic was proposed for reconciling hesitant or conflicting assessments in fuzzy control and decision-making.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.22900] Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
[Submitted on 21 May 2026]
Title:Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
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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.
Comments: 30 pages, 1 figure
Subjects:
Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Quantum Physics (quant-ph)
Cite as: arXiv:2605.22900 [cs.AI]
(or arXiv:2605.22900v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.22900
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Oscar Humberto Montiel [view email] [v1] Thu, 21 May 2026 17:26:53 UTC (53 KB)
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