Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914590172905472 |
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| author | Ross, Oscar Montiel |
| author_facet | Ross, Oscar Montiel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions Ross, Oscar Montiel Artificial Intelligence Logic in Computer Science Quantum Physics 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. |
| title | Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions |
| topic | Artificial Intelligence Logic in Computer Science Quantum Physics |
| url | https://arxiv.org/abs/2605.22900 |