TL;DR
This paper explores operators generated by fuzzy relations, providing representation theorems, algebraic models, and applications in non-classical logic, formal concept analysis, and Pavelka's algebras.
Contribution
It introduces new representation theorems and algebraic models for operators induced by fuzzy relations, expanding their theoretical and practical applications.
Findings
Representation theorems for fuzzy relation operators
Algebraic models with semantics for non-classical logic
Applications to Pavelka's algebras
Abstract
Theory of operators generated by binary fuzzy relations is highly increasing for its nature and applicability. The main goal of the paper is to present several representation theorems for operators induced by fuzzy relations (for example closure operators used in formal concept analysis, monadic operators or tense operators). Consequently we establish algebraic models with their semantics which are usable in the non-classical logic research and in the computer science research. The obtained results are applied in the theory of Pavelka's algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Multi-Criteria Decision Making