Q-Filters of Quantum B-Algebras and Basic Implication Algebras
AbstractThe concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established. View Full-Text
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Zhang, X.; Borzooei, R.A.; Jun, Y.B. Q-Filters of Quantum B-Algebras and Basic Implication Algebras. Symmetry 2018, 10, 573.
Zhang X, Borzooei RA, Jun YB. Q-Filters of Quantum B-Algebras and Basic Implication Algebras. Symmetry. 2018; 10(11):573.Chicago/Turabian Style
Zhang, Xiaohong; Borzooei, Rajab A.; Jun, Young B. 2018. "Q-Filters of Quantum B-Algebras and Basic Implication Algebras." Symmetry 10, no. 11: 573.
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