非交换剩余格上模糊极滤子的特征与性质
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摘要
运用模糊集的运算方法和原理,在非交换剩余格上引入了模糊极滤子的概念,并研究了其表示定理和特征性质,获得了在一定条件下非交换剩余格上模糊极滤子与模糊子正蕴涵滤子相互等价的结论.研究结果进一步拓展了非交换剩余格上的模糊滤子理论,为其在逻辑代数及计算机信息处理等方面的应用奠定了理论基础.
By using the principles and methods of fuzzy sets, in this paper, the concept of "fuzzy fantastic filter" is introduced in the non-commutative residuated lattice. By studying its properties and characterizations, the equivalent representation theorems under certain conditions are given between the fuzzy fantastic filter and the fuzzy sub positive implicative filter. The results of the study further extend the fuzzy filter theory of the non-commutative residuated lattice, and lay a theoretical foundation for the application of algebraic logic and computer information processing.
By using the principles and methods of fuzzy sets, in this paper, the concept of "fuzzy fantastic filter" is introduced in the non-commutative residuated lattice. By studying its properties and characterizations, the equivalent representation theorems under certain conditions are given between the fuzzy fantastic filter and the fuzzy sub positive implicative filter. The results of the study further extend the fuzzy filter theory of the non-commutative residuated lattice, and lay a theoretical foundation for the application of algebraic logic and computer information processing.
引文
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[8] SHOKOOFEH G.Obstinate,Weak Implicative and Fantastic Filter of Non-Commutative Residuated Lattices [J].Afrika Matematika,2017,28(1-2):68-84.
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[10] BAKHSHI M.Generalized Fuzzy Filter in Non-Commutative Residuated Lattices [J].Afrika Matematika,2014,25(2):289-305.
[2] DINOLA A,GEORGESCU G.Pseudo-BL-Algebras:Part I [J].Mult-Valued Log,2002,8(5-6):673-714.
[3] ZHU Y Q,XU Y.On Fliter Theory of Residuated Lattices [J].Information Sciences,2010,180(19):3614-3632.
[4] WANG W,Xin X L.On Fuzzy Filters of Pseudo-BL-Algebras [J].Fuzzy Sets and Systems,2011,162(4):27-38.
[5] 刘莉君.剩余格上几类n重模糊滤子的等价刻画 [J].西南大学学报(自然科学版),2017,39(9):107-112.
[6] WANG W,XU Y,TONG D,et al.Some Results on Fuzzy Weak Boolean Filters of Non-Commutative Residuated Lattices [J].Springer India,2014,250:97-103.
[7] GASSE B,DESCHRIJVER G,CORNELIS C,et al.Filter of Residuated Lattices and Triangle Algebras [J].Information Sciences,2010,180(16):3006-3020.
[8] SHOKOOFEH G.Obstinate,Weak Implicative and Fantastic Filter of Non-Commutative Residuated Lattices [J].Afrika Matematika,2017,28(1-2):68-84.
[9] DUMITRU B,DANA P.A New Approach for Classification of Filter in Residuated Lattices [J].Fuzzy Sets and Systems,2015,260:121-130.
[10] BAKHSHI M.Generalized Fuzzy Filter in Non-Commutative Residuated Lattices [J].Afrika Matematika,2014,25(2):289-305.