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Information Sciences, ISSN 0020-0255, 09/2018, Volume 460-461, pp. 190 - 201
Skew lattices are one of the most successful non-commutative generalizations of lattices. Motivated by the study of residuation on ordered structures and that... 
Conormal | Skew lattices | Residuated skew lattices | Skew BL-algebras | Skew MTL-algebras | Join-bidistributive | FUZZY LOGIC | COMPUTER SCIENCE, INFORMATION SYSTEMS | Algebra
Journal Article
SOFT COMPUTING, ISSN 1432-7643, 01/2020, Volume 24, Issue 1, pp. 247 - 258
The notion of n-normal residuated lattice, as a subclass of residuated lattices in which every prime filter contains at most n minimal prime filters, is... 
Coannihilator | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Reticulation | REPRESENTATIONS | Residuated lattice | omega-filter | Normal residuated lattice | n-normal residuated lattice | Coannulet | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal Article
Information Sciences, ISSN 0020-0255, 01/2013, Volume 218, pp. 194 - 204
This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing lower and upper sets. In particular, it is shown that when the... 
Lower (upper) set | Fuzzy rough set | Residuated lattice | Fuzzy topology | COMPUTER SCIENCE, INFORMATION SYSTEMS | SPACES
Journal Article
Logic Journal of the IGPL, ISSN 1367-0751, 2018, Volume 26, Issue 5, pp. 475 - 504
Journal Article
Soft Computing, ISSN 1432-7643, 8/2015, Volume 19, Issue 8, pp. 2083 - 2094
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 4/2019, Volume 157, Issue 2, pp. 434 - 458
The order dual $${[{\rm Fil}{R_{R}}]^{{\rm du}}}$$ [ Fil R R ] du of the set $${{\rm Fil}{R_{R}}}$$ Fil R R of all right topologizing filters on a fixed but... 
localization | 13F05 | primary 16S90 | Mathematics | 16P50 | congruence | secondary 06F05 | residuated lattice | Dedekind domain | topologizing filter | lattice ordered monoid | Mathematics, general | Prüfer domain | MATHEMATICS | Prufer domain
Journal Article
IRANIAN JOURNAL OF FUZZY SYSTEMS, ISSN 1735-0654, 12/2019, Volume 16, Issue 6, pp. 107 - 126
In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and... 
MATHEMATICS | directly indecomposable algebra | MATHEMATICS, APPLIED | Boolean element | free algebras | (Semi) divisible residuated lattice | LOGIC
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 10/2019, Volume 373, pp. 62 - 77
The aim of this paper is to investigate some weaker versions of topological residuated lattices, which are para-∧-topological residuated lattices (∧... 
M-system | (⊙, →, adjoint) compatible | Para(semi)-topological residuated lattice | Filter | Residuated lattice | (⊙ → adjoint) compatible | MATHEMATICS, APPLIED | ALGEBRAS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | LOGIC | (circle dot, ->, adjoint) compatible
Journal Article
International Journal of Approximate Reasoning, ISSN 0888-613X, 01/2015, Volume 56, pp. 28 - 42
Journal Article
Journal Article
Information Sciences, ISSN 0020-0255, 2010, Volume 180, Issue 19, pp. 3614 - 3632
Journal Article
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, ISSN 1224-1784, 2019, Volume 27, Issue 1, pp. 245 - 268
In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green's... 
Residuated skew lattice | Green’s relation | (skew) deductive system | Variety | Residuated lattice | Skew lattice | MATHEMATICS | MATHEMATICS, APPLIED | residuated lattice | residuated skew lattice | variety | Green's relation
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 04/2018, Volume 336, pp. 54 - 86
Journal Article
Algebra universalis, ISSN 0002-5240, 12/2018, Volume 79, Issue 4, pp. 1 - 26
We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one... 
Algebra | 03B50 | Residuated lattice | Classification of kites | Mathematics | Subdirect irreducible kite | 03G10 | Kite algebra | MATHEMATICS | MV-ALGEBRAS | BL-ALGEBRAS
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 07/2013, Volume 222, pp. 78 - 83
We replace the so-called adjointness in the definition of residuated lattice by its strict version where inequalities are replaced by equalities. We prove that... 
Skew residuated lattice | Divisibility semiloop | Reversion | Sectional involution | Difference property | Adjointness property | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Algebra
Journal Article
Soft Computing, ISSN 1432-7643, 05/2017, Volume 21, Issue 10, pp. 2561 - 2574
In this paper, we present an investigation of quantale algebras (Q-algebras for short) as lattice-valued quantales (Q-quantales for short). First, we prove... 
Quantale algebra | Q-ordered set | Quantale | Lattice-valued quantale | COMPLETIONS | LOGIC | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ORDERED SEMIGROUPS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RESIDUATED LATTICES | CATEGORY | FUZZY IDEALS | SETS
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 11/2016, Volume 303, pp. 128 - 135
Di Nola and Gerla showed that MV-algebras and coupled semirings are in a natural one-to-one correspondence. We generalize this correspondence to residuated... 
Double negation law | Semiring | General coupled semiring | Residuated lattice | MATHEMATICS, APPLIED | ALGEBRAS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Algebra | Mathematics - Rings and Algebras
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 03/2020, Volume 382, pp. 120 - 128
This paper aims to solve the question “whether there is a residuated EQ-algebra, which is not a residuated lattice?” In this paper, we first introduce the... 
EQ-algebra | Residuated lattice | Residuated meet semilattice monoid | MATHEMATICS, APPLIED | PREFILTERS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 04/2018, Volume 336, pp. 87 - 115
Axiomatic characterization of approximation operators plays an important role in the study of rough set theory. Different axiom sets of abstract operators can... 
L-fuzzy rough sets | Approximation operators | Residuated lattices | Axioms | Rough sets | MATHEMATICS, APPLIED | ALGEBRAS | SETS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | LOGIC
Journal Article
International Journal of General Systems, ISSN 0308-1079, 11/2016, Volume 45, Issue 7-8, pp. 773 - 789
We deal with size reduction of concept lattices by means of factorization by block relations defined on corresponding formal context. We show that all block... 
complete residuated lattice | formal concept analysis | fuzzy logic | Block relation | complete tolerance | HEDGES | COMPUTER SCIENCE, THEORY & METHODS | Fuzzy logic | Algorithms | Design engineering | Multiplication | Size reduction | Lattices | Design analysis | Factorization | Predicate logic
Journal Article
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