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2006•Mohu xitong yu shuxueRequires access

The Simplified Forms of Definition of MV-algebra

WU Hong-bo

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Abstract

Through study of MV-algebra and the Lukasiewicz propositional calculus system, we have simplified the definition of MV-algebra and investigated the relation among some logic algebras.the main results of the paper are: (1) Two equlvalent simplifies forms of MV-algebra are obtained; (2) The concept of Weak Lattice Implication-Algebra is proposed, and the equivalence between BR_0-algebra and Weak Lattice Implication-Algebra is proved; (3) It is proved that Weak Lattice Implication-Algebra is Regular Fuzzy Implication-Algebra.

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Through study of MV-algebra and the Lukasiewicz propositional calculus system, we have simplified the definition of MV-algebra and investigated the relation among some logic algebras.the main results of the paper are: (1) Two equlvalent simplifies forms of MV-algebra are obtained; (2) The concept of Weak Lattice Implication-Algebra is proposed, and the equivalence between BR_0-algebra and Weak Lattice Implication-Algebra is proved; (3) It is proved that Weak Lattice Implication-Algebra is Regular Fuzzy Implication-Algebra.

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Available abstract

Through study of MV-algebra and the Lukasiewicz propositional calculus system, we have simplified the definition of MV-algebra and investigated the relation among some logic algebras.the main results of the paper are: (1) Two equlvalent simplifies forms of MV-algebra are obtained; (2) The concept of Weak Lattice Implication-Algebra is proposed, and the equivalence between BR_0-algebra and Weak Lattice Implication-Algebra is proved; (3) It is proved that Weak Lattice Implication-Algebra is Regular Fuzzy Implication-Algebra.

Key concepts: Mathematics, Algebra over a field, Cellular algebra, Equivalence (formal languages), Lattice (music), Quotient algebra, Filtered algebra, Term algebra

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