基于赋范格H 蕴涵代数的性质

Abstract

Abstract:

Firstly, in this paper, under a norm situation, the notion of lattice H implication algebra L^[15]is extended (i.e., normed lattice H implication algebras), and some properties are discussed. Secondly, with the properties of implication distance d_→, v -distance d_v and ∧-distance d in normed lattice H implication algebras L investigated, the authors also define norned implication epimorphism、normed lattice H implication
homomorphism、normed lattice H implication isomorphism and normed isomorphism by using of a mapping f which has two normed lattice H implication algebras L₁ and L₂ together with its properties studied. Finally, the authors further probe into the boundedness
of convergence sequence, showing that sequences operations (i.e., $\otimes$ , $\oplus$ , ∨, ∧, →) to implication distance is bounded.

Key words: Normed lattice H implication algebra, Implication distance, Normed implication homomorphism, Normed isomorphism, Boundedness

CLC Number:

03B50

LAI Jia-Jun, XU Yang, QIN Ke-Yun. The Properties of Normed Lattice H Implication Algebras[J].Acta mathematica scientia,Series A, 2010, 30(6): 1465-1473.

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The Properties of Normed Lattice H Implication Algebras

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