非交换剩余格上模糊滤子的等价刻画
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摘要
运用区间模糊集的概念和方法,在非交换剩余格上引入了模糊极滤子和模糊弱蕴涵滤子的概念,并获得了非交换剩余格上模糊极滤子与模糊弱蕴涵滤子相互等价的条件。研究结果拓展了非交换剩余格上的模糊滤子理论,也为研究非经典逻辑系统的结构奠定了理论基础。
By using the principle and method of fuzzy sets. In this paper, we introduce the notions of fuzzy fantastic filters and fuzzy weak implicative filters on non-commutative residuated lattice and study their properties. Some equivalent representation theorems under certain conditions are obtained between the fuzzy fantastic filter and the fuzzy weak implicative filter. The results of the study further extend the fuzzy filter theory of the non-commutative residuated lattice, it lays a theoretical foundation for nonclassical logic system.
By using the principle and method of fuzzy sets. In this paper, we introduce the notions of fuzzy fantastic filters and fuzzy weak implicative filters on non-commutative residuated lattice and study their properties. Some equivalent representation theorems under certain conditions are obtained between the fuzzy fantastic filter and the fuzzy weak implicative filter. The results of the study further extend the fuzzy filter theory of the non-commutative residuated lattice, it lays a theoretical foundation for nonclassical logic system.
引文
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[2] Georgescu G.Pseudo-MV algebras[J].Mult-Valued Log,2001,6(1～2):95～135.
[3] Dinola A,Georgescu G.Pseudo-BL-algebras:Part I[J].Mult-Valued Log,2002,8(5～6):673～714.
[4] Bakhshi M.Generalized fuzzy filter in non-commutative residuated lattices[J].Afrika Matematika,2014,25(20):289～305.
[5] 刘莉君.基于可交换剩余格上几类n重模糊滤子及其性质[J].模糊系统与数学,2018,32(1):60～65.
[6] Liu L Z.Boolean filter and positive implicative filter of non-commutative residuated lattices[J].Information Sciences,2007,177(25):5725～5738.
[7] Ghorbani S.Weak boolean filters of non-commutative residuated lattice[J].World Appl.Sci.J,2011,12(1):586～590.
[8] Obstinate S G.Weak implicative and fantastic filter of non-commutative residuated lattices[J].Afrika Matematika,2017,28(1～2):68～84.
[9] Gasse B,Deschrijver G.Filter of residuated lattices and triangle algebras[J].Information Sciences,2010,180(16):3006～3020.
[10] Michiro K A.Filter in non-commutative residuated lattice[J].Ssientiae Mathematicae Japonicae,2013,76(2):217～225.