Abstract
The aim of this paper is to investigate several operators on quantum B-algebras. At first, we introduce closure and interior operators on quantum B-algebras and consider their relations on bounded quantum B-algebras. Furthermore, we discuss very true operators on quantum B-algebras by three cases via the unit element, and present some similar conclusions and different results. Finally, by constructing a very true operator on a quotient very true perfect quantum B-algebra, we establish a homomorphism theorem on very true perfect quantum B-algebras.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
We establish a homomorphism theorem on very true perfect quantum B-algebras (Theorem 3)
We study closure operators and very true operators on quantum
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Quantum B-algebras have two kinds of binary operations, they have symmetry, so when studying some properties of quantum B-algebras, in some cases, it is enough to study only one operation, which makes the study simple and effective. It presented a positive answer to the question of “whether natural axiomatization is possible and to what extent the standard methods of mathematical logic can capture this fuzzy logic” It has been successful in several different tasks in various logical algebras, such as MV-algebras [9], Rl-monoids [10], pseudo-BCK algebras [11], effect algebras [12] and equality algebras [13]. In this paper, we consider very true operators on quantum B-algebras in three cases and analyse their different properties, whose results will unify and enrich previous works on very true operators of quantum structure. We establish a homomorphism theorem on very true perfect quantum B-algebras (Theorem 3)
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