# Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions

arXiv: https://arxiv.org/abs/2605.22900 · HTML: https://mlsanity.com/paper/2605.22900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 40 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 1 of 1)

- [Foundations of Quantum Granular Computing with Effect-Based Granules, Algebraic Properties and Reference Architectures](https://mlsanity.com/paper/2511.22679/) (2025)

## Abstract (arXiv)

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.