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A Residuated Lattice of L-Fuzzy Subalgebras of a Mono-Unary Algebra
New Mathematics and Natural Computation, 2019Given a complete residuated lattice [Formula: see text] and a mono-unary algebra [Formula: see text], it is well known that [Formula: see text] and the residuated lattice [Formula: see text] of [Formula: see text]-fuzzy subsets of [Formula: see text ...
S. V. T. Foka, Marcel Tonga
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On ideals of residuated lattices
Journal of Intelligent & Fuzzy Systems, 2021In this paper, we first point out some mistakes in [12]. Especially the Theorem 3.9 [12] showed that: Let A be residuated lattice and ∅ ≠ X ⊆ A, then the least ideal containing X can be expressed as: 〈X〉 = {a ∈ A|a ≤ (·· · ((x1 ⊕ x2) ⊕ x3) ⊕ ·· ·) ⊕ xn, xi ∈ X, i = 1, 2 ·· · , n}. But we present an example to illustrate the ideal generation formula may
Yan Yan Dong, Jun Tao Wang
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Categories of Automata and Languages Based on a Complete Residuated Lattice
New Mathematics and Natural Computation, 2018The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category.
Vinay Gautam +3 more
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Topological residuated lattices
Soft Computing, 2020The notion of a (semi)topological residuated lattice is introduced, and its properties are investigated. Some separation axioms on topological residuated lattices are studied. The notion of completion of a residuated lattice is introduced and characterized by means of the inverse limit of an inverse system.
Saeed Rasouli, Amin Dehghani
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On pseudo residuated skew lattices [PDF]
Boletín de la Sociedad Matemática Mexicana, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Koohnavard, A. Borumand Saeid
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Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids
Algebra Universalis, 2019We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-ordered groupoids are both EXPTIME-complete.
D. Shkatov, C. J. Alten
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Lattice logic as a fragment of (2-sorted) residuated modal logic
J. Appl. Non Class. Logics, 2018Correspondence and Shalqvist theories for Modal Logics rely on the simple observation that a relational structure is at the same time the basis for a model of modal logic and for a model of first-order logic with a binary predicate for the accessibility ...
Chrysafis Hartonas
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Residuated lattices and lattice effect algebras
Fuzzy Sets and Systems, 2007Residuated lattices and lattice effect algebras arose in two rather different fields. In this paper, by introducing two partial operations in effect algebras, we investigate the mutual relationship between involutive residuated lattices and lattice effect algebras.
Qingguo Li, Xiangnan Zhou, Guo-Jun Wang
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Fuzzy Sets and Systems, 2013
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 such structures, called skew residuated lattices, can be characterized as lattices with certain involutions in principal filters.
I. Chajda, J. KrňáVek
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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 such structures, called skew residuated lattices, can be characterized as lattices with certain involutions in principal filters.
I. Chajda, J. KrňáVek
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Information Sciences, 2018
Abstract Skew lattices are one of the most successful non-commutative generalizations of lattices. Motivated by the study of residuation on ordered structures and that of skew Boolean algebras and skew Heyting algebras, in this paper, we introduce the concept of residuated skew lattices as a new non-commutative version of residuated lattices.
Xiangnan Zhou, Yuan Zhi, Qingguo Li
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Abstract Skew lattices are one of the most successful non-commutative generalizations of lattices. Motivated by the study of residuation on ordered structures and that of skew Boolean algebras and skew Heyting algebras, in this paper, we introduce the concept of residuated skew lattices as a new non-commutative version of residuated lattices.
Xiangnan Zhou, Yuan Zhi, Qingguo Li
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