Localization of k × j-rough Heyting algebras
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Federico Almiñana
Abstract
k-rough Heyting algebras were introduced by Eric San Juan in 2008 as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. In 2020, we defined and studied the variety of k × j-rough Heyting algebras. These algebras constitute an extension of Heyting algebras and in the case j = 2 they coincide with k-rough Heyting algebras. In this note, we introduce the notion of k × j-ideal on k × j-rough Heyting algebras which allows us to consider a topology of them. Besides, we define the concept of 𝓕-multiplier, where 𝓕 is a topology on a k × j-rough Heyting algebra A, which is used to construct the localization k × j-rough Heyting algebras A𝓕. Furthermore, we prove that the k × j-rough Heyting algebras of fractions AS associated with a ∧ -closed subset S of A is a k × j-rough Heyting algebra of localization. Finally, in the finite case we prove that AS is isomorphic to a special subalgebra of A. Since 3-valued Łukasiewicz –Moisil algebras are a particular case of k × j-rough Heyting algebras, all these results generalize those obtained in 2005 by Chirtes and Busneag.
Federico Almiñana thanks the institutional support of Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
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Communicated by Roberto Giuntini
Acknowledgement
The authors acknowledge many helpful comments from the anonymous referee, which considerably improved the presentation of this paper.
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- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
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- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
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- Prediction of the exponential fractional upper record-values
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Articles in the same Issue
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
