Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
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
Fundamenta Informaticae
Fuzzy sets and sheaves. Part I
Fuzzy Sets and Systems
Mathematical Logic
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
What is mathematical fuzzy logic
Fuzzy Sets and Systems
Which logic is the real fuzzy logic?
Fuzzy Sets and Systems
Pointed semi-quantales and lattice-valued topological spaces
Fuzzy Sets and Systems
On fuzzy filters of pseudo BL-algebras
Fuzzy Sets and Systems
EQ-logics: Non-commutative fuzzy logics based on fuzzy equality
Fuzzy Sets and Systems
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
Studia Logica
EQ-algebras from the point of view of generalized algebras with fuzzy equalities
Fuzzy Sets and Systems
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We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. These algebras are intended to become algebras of truth values for a higher-order fuzzy logic (a fuzzy type theory, FTT). The motivation stems from the fact that until now, the truth values in FTT were assumed to form either an IMTL-, BL-, or MV-algebra, all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation (multiplication) and its residuum. The latter is a natural interpretation of implication in fuzzy logic; the equivalence is then interpreted by the biresiduum, a derived operation. The basic connective in FTT, however, is a fuzzy equality and, therefore, it is not natural to interpret it by a derived operation. This defect is expected to be removed by the class of EQ-algebras introduced and studied in this paper. From the algebraic point of view, the class of EQ-algebras generalizes, in a certain sense, the class of residuated lattices and so, they may become an interesting class of algebraic structures as such.