Mediative Fuzzy Logic Extended to Type-2, Type-3, and Quantum Systems
A recent paper on arXiv (2605.22900) presents a comprehensive framework for Mediative Fuzzy Logic, broadening its scope from type-1 to include interval type-2, granular type-3, and quantum variations. The mediative operator is defined as a convex aggregation influenced by hesitation and contradiction. Mediative truth values are represented as independent pairs of truth and falsity within a continuous bilattice-like framework. The study introduces a propositional system that enhances traditional t-norm-based fuzzy logic through a mediative connective. It confirms soundness, paraconsistency, and conservativity regarding the foundational fuzzy base for formulas lacking mediation. Additionally, coherent semantic extensions are developed for interval type-2 truth values and evaluations indexed by granules.
Key facts
- arXiv:2605.22900v1
- Mediative Fuzzy Logic conceived for reconciling hesitant or conflicting assessments
- Unified account of type-1 core, interval type-2, granular type-3, and quantum extensions
- Mediative operator characterized as convex aggregation controlled by hesitation and contradiction
- Mediative truth values modeled as independent truth-falsity pairs in continuous bilattice-like structure
- Propositional system extends standard t-norm-based fuzzy logic with mediative connective
- Soundness, paraconsistency, and conservativity established for formulas without mediation
- Semantic extensions formulated for interval type-2 truth values and granule-indexed local evaluations
Entities
Institutions
- arXiv