Theoretical Computer Science
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets
Information Sciences: an International Journal
An enriched category approach to many valued topology
Fuzzy Sets and Systems
Uniform environments as a general framework for metrics and uniformities
Fuzzy Sets and Systems
Fuzzy radicals and prime fuzzy ideals of ordered semigroups
Information Sciences: an International Journal
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Fuzzy logics from substructural perspective
Fuzzy Sets and Systems
MTL-algebras arising from partially ordered groups
Fuzzy Sets and Systems
Implication structures, fuzzy subsets, and enriched categories
Fuzzy Sets and Systems
Pointed semi-quantales and lattice-valued topological spaces
Fuzzy Sets and Systems
From quantale algebroids to topological spaces: Fixed- and variable-basis approaches
Fuzzy Sets and Systems
Categorical approaches to non-commutative fuzzy logic
Fuzzy Sets and Systems
Formal concept analysis and lattice-valued Chu systems
Fuzzy Sets and Systems
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In this paper, we investigate some properties of nuclei and conuclei on residuated lattices and their concrete structures. By means of nuclei and conuclei we give the respective characterizations for a residuated lattice reducing to a generalized MV-algebra and a generalized BL-algebra. Based on studying regular commutative bounded integral residuated lattices, we introduce the concept of a pseudo-dual quantale and investigate some properties of it, and prove that the set of fuzzy sets of a nonempty set equipped with multiplication and negation operations is a commutative Girard quantale. Finally, we discuss the relationship between quantic nuclei and quantic conuclei on a pseudo-dual quantale, and show that the quantic nuclei and the ideal conuclei on a pseudo-Girard quantale are in one-to-one correspondence.