Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
A similarity-based generalization of fuzzy orderings preserving the classical axioms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Propositional calculus under adjointness
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Associatively tied implications
Fuzzy Sets and Systems - Theme: Basic concepts
A characterization of fuzzy implications generated by generalized quantifiers
Fuzzy Sets and Systems
Mathematical Logic
On copulas, quasicopulas and fuzzy logic
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (1143 - 1198) " Distributed Bioinspired Algorithms"; Guest editors: F. Fernández de Vega, E. Cantú-Paz
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Fuzzy Sets and Systems
The logic of tied implications, part 1: Properties, applications and representation
Fuzzy Sets and Systems
EQ-logics: Non-commutative fuzzy logics based on fuzzy equality
Fuzzy Sets and Systems
Reasoning about mathematical fuzzy logic and its future
Fuzzy Sets and Systems
Elements of model theory in higher-order fuzzy logic
Fuzzy Sets and Systems
Formal concept analysis and lattice-valued Chu systems
Fuzzy Sets and Systems
EQ-algebras from the point of view of generalized algebras with fuzzy equalities
Fuzzy Sets and Systems
| Hi-index | 0.20 |
A special algebra called EQ-algebra has been recently introduced by Vilem Novak. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations - meet, multiplication, and fuzzy equality - and a unit element. They open the door to an alternative development of fuzzy (many-valued) logic with the basic connective being a fuzzy equality instead of an implication. This direction is justified by the idea presented by G.W. Leibniz that ''a fully satisfactory logical calculus must be an equational one.'' In this paper, we continue the study of EQ-algebras and their special cases. We introduce and study the prefilters and filters of separated EQ-algebras. We give great importance to the study of good EQ-algebras. As we shall see in this paper, the ''goodness'' property (and thus separateness) is necessary for reasonably behaving algebras. We enrich good EQ-algebras with a unary operation @D (the so-called Baaz delta), fulfilling some additional assumptions that are heavily used in fuzzy logic literature. We show that the characterization theorem obtained until now for representable good EQ-algebras also hold for the enriched algebra.