拟BCK-代数的扰动模糊理想
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摘要
引入了拟BCK-代数的扰动模糊理想的概念,刻画了拟BCK-代数的扰动模糊理想的特征;给出拟BCK-代数上的一个扰动模糊集成为扰动模糊理想的条件;构造了由给定扰动模糊集生成的最小扰动模糊理想;研究了拟BCK-代数的扰动模糊理想的同态性质。
The concept of disturbing fuzzy ideals of pseudo-BCK algebras is introduced,the characterizations of disturbing fuzzy ideals of a pseudo-BCK algebra are described.The conditions for a disturbing fuzzy set of a pseudo-BCK algebra to be a disturbing fuzzy ideal are given.Given a disturbing fuzzy set A of a pseudo-BCK algebra,the least disturbing fuzzy ideal containing A is constructed.The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are studied.
The concept of disturbing fuzzy ideals of pseudo-BCK algebras is introduced,the characterizations of disturbing fuzzy ideals of a pseudo-BCK algebra are described.The conditions for a disturbing fuzzy set of a pseudo-BCK algebra to be a disturbing fuzzy ideal are given.Given a disturbing fuzzy set A of a pseudo-BCK algebra,the least disturbing fuzzy ideal containing A is constructed.The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are studied.
引文
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[17]Xi O G.Fuzzy BCK-algebras[J].Math.Japon.,1991,36(5):935~942.
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[20]Peng J Y.On intuitional fuzzyifying ideals in BCK-algebra based on L*-lattice valued logic[J].Journal of Systems Science and Mathemtical Science,2010,30(4):556~576.
[21]彭家寅.直觉模糊BCK-代数[J].淮阴师范学院学报,2011,10(4):296~303.
[22]Peng J Y.Vague BCK-algebra[C].2010 3rd International Conference on Advanced Computer Theory and Engineering,2010,2:271~275.
[23]Yamak S,Kazanci O,Davvaz B.Applications of interval-valued t-norms(t-conorms)to fuzzy n-ary subhypergroups[J].Information Sciences,2008,178:3957~3972.
[24]刘熠,钟纯真.格蕴涵代数的区间值-模糊滤子理论[J].模糊系统与数学,2013,27(4):74~83.
[25]韩莹,陈森发,陈胜.TD型扰动模糊正规子群[J].模糊系统与数学,2006,20(5):25~29.
[2]Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87~96.
[3]Gau W L,Buehrer D J.Vague sets[J].IEEE Transactions on Systems,Man,and Cybernetics,1993,23(2):610~614.
[4]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning[J].Information Sciences,1975,8(2):199~249.
[5]王元元.计算机科学中的现代逻辑学[M].北京:科技出版社,2001:207.
[6]Lin T L.A set theory for soft computing[C].Proceeding of 1996IEEE International Conference on Fuzzy Systems,1996:1140~1146.
[7]Ying M S.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1995,1(5):625~629.
[8]刘心,陈图云.扰动模糊逻辑及其“非算子”[J].模糊系统与数学,2002,16(2):179~182.
[9]Chang C C.Algebraic analysis of many valeued logics[J].Trans.Amer.Math.Soc.,1958,88:467~490.
[10]Imai Y,Iséki K.On axiom systems of propositional calculi XIV[J].Proc.Japan Academy,1966,42:19~22.
[11]Hájek P.Metamathematics of fuzzy logic[M].Kluwer Acad.Publ.,Dordrecht,1998.
[12]Georgescu G,Iorgulescu A.Pseudo-MV algebras:a noncommutative extension of MV algebras[C].The Proc.of the Fourth International Symp.on Economic Informatics,Bucharest,Romania,May 1999:961~968.
[13]Rachunek J.A non-commutative generalization of MV algebras[J].Czechoslovak Math.J.,2002,52:255~273.
[14]Georgescu G,Iorgulescu A.Pseudo-BL algebras:a noncommutative extension of BL algebras[C].Abstracts of the Fifth International conference FSTA 2000,Slovakia,February 2000:90~92.
[15]Georgescu G,Iorgulescu A.Pseudo-BCK algebras:an extension of BCK algebras[C].Proc.of DMTCS′01:Combinatorics,Computability and Logic,Springer,London,2001:97~114.
[16]Jun Y B.Characterizations of pseudo-BCK algebras[J].Sci.Math.Jpn.,2003,57:265~270.
[17]Xi O G.Fuzzy BCK-algebras[J].Math.Japon.,1991,36(5):935~942.
[18]Dymek G,Walendziak A.Fuzzy ideals of pseudo-BCK algebras[J].Demonstratio Mathematica,2012,XLV(1):1~15.
[19]Jun Y B.Fuzzy pseudo-ideals of pseudo-BCK algebras[J].Journal of Applied Mathematics and Computing,2003,12(1):243~250.
[20]Peng J Y.On intuitional fuzzyifying ideals in BCK-algebra based on L*-lattice valued logic[J].Journal of Systems Science and Mathemtical Science,2010,30(4):556~576.
[21]彭家寅.直觉模糊BCK-代数[J].淮阴师范学院学报,2011,10(4):296~303.
[22]Peng J Y.Vague BCK-algebra[C].2010 3rd International Conference on Advanced Computer Theory and Engineering,2010,2:271~275.
[23]Yamak S,Kazanci O,Davvaz B.Applications of interval-valued t-norms(t-conorms)to fuzzy n-ary subhypergroups[J].Information Sciences,2008,178:3957~3972.
[24]刘熠,钟纯真.格蕴涵代数的区间值-模糊滤子理论[J].模糊系统与数学,2013,27(4):74~83.
[25]韩莹,陈森发,陈胜.TD型扰动模糊正规子群[J].模糊系统与数学,2006,20(5):25~29.