BCK代数的扰动模糊理想
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摘要
将扰动模糊集用于BCK-代数中,引入BCK-代数的扰动模糊子代数、扰动模糊左右约简理想、扰动模糊理想和扰动模糊蕴涵理想的概念,并研究其性质及关系.
The disturbing fuzzy set is applied to BCK-algebras,and by introduction of the concepts of disturbing fuzzy sub-algebras,disturbing fuzzy left/right reduced ideals,disturbing fuzzy ideals and disturbing fuzzy implicative ideals,the properties and relations among them are examined.
The disturbing fuzzy set is applied to BCK-algebras,and by introduction of the concepts of disturbing fuzzy sub-algebras,disturbing fuzzy left/right reduced ideals,disturbing fuzzy ideals and disturbing fuzzy implicative ideals,the properties and relations among them are examined.
引文
[1]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338-353.
[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 Confer-ence 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].Transactions of the American Mathematic Society,1958,88:467-490.
[10]Imai Y,Iseki K.On axiom systems of propositional calculi XIV[J].Proceedings of the Japan Academy,1966,42:19-22.
[11]Iseki K,Tanaka S.Ideal theory of BCK-algebra[J].Mathematica Japonica,1976,2:351-336.
[12]Lei T D,Pu T H.BCK-algebra and BCI-algebra[Z].Lecuture in Shanxi Normal University,1983.
[13]Iseki K.Some properties of BCK-algebras[J].Mathematic Seminar Notes,1974,2:193-201.
[14]Hajek P.Metamathematics of fuzzy logic[M].Kluwer Acad.Publish.,Dordrecht,1998.
[15]Georgescu G,Iorgulescu A.Pseudo-MV algebras:a noncommutative extension of MV algebras[C].The Proceeding of the Fourth International Symposium.on Economic Informatics,Bucharest,Romania,May1999:961-968.
[16]Rachunek J.A non-commutative generalization of MV algebras[J].Czechoslovak Mathematical Joumal,2002,52:255-273.
[17]Rosenfeld A.Fuzzy group[J].Journal Of Mathematical Analysis And Applications,1971,35:512-517.
[18]Dib K A,Galhum N.Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups[J].Fuzzy Sets and Systems,1997,92:103-111.
[19]Mukherjee T K,Sen M K.On fuzzy ideals in ring(I)[J].Fuzzy Sets and Systems,1987,21:99-104.
[20]Chang C L.Fuzzy topological spaces[J].Journal of Mathematical Analysis And Applications,1968,24:182-190.
[21]彭家寅.Q-代数中具有界限的模糊子代数(英文)[J].内江师范学院学报,2011,26(8):1-5.
[22]Xi O G.Fuzzy BCK-algebras[J].Mathematica Japonica,1991,36(5):935-942.
[23]彭家寅.BCK-代数的(s,t]-模糊子代数与R-模糊代数[J].内江师范学院学报,2015,30(6):1-10.
[24]彭家寅.BCK-代数的Ω-模糊代数理想[J].内江师范学院学报,2008,23(4):5-7.
[25]Dymek G,Walendziak A.Fuzzy ideals of pseudo-BCK algebras[J].Demonstratio Mathematica,2012,XLV(1):1-15.
[26]Jun Y B.Fuzzy pseudo-ideals of pseudo-BCK algebras[J].Journal of Applied Mathematics and Computing,2003,12(1):243-250.
[27]彭家寅.直觉模糊BCK-代数[J].淮阴师范学院学报,2011,10(4):296-303.
[28]彭家寅.Vague B-代数(英文)[J].内江师范学院学报,2012,27(4):1-5.
[29]Yamak S,Kazanci O,Davvaz B.Applications of interval-valued t-norms(t-conorms)to fuzzy n-ary sub-hypergroups[J].Information Sciences,2008,178:3957-3972.
[30]彭家寅.区间值(∈,∈∨q)-模糊B-代数(英文)[J].内江师范学院学报,2012,27(2):1-4.
[31]彭家寅.LA-半群中的区间值(∈,∈∨q)-模糊理想[J].内江师范学院学报,2015,30(10):1-9.
[32]彭家寅.LA-半群中的区间值-模糊理想(英文)[J].内江师范学院学报,2015,30(8):1-10.
[33]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 Confer-ence 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].Transactions of the American Mathematic Society,1958,88:467-490.
[10]Imai Y,Iseki K.On axiom systems of propositional calculi XIV[J].Proceedings of the Japan Academy,1966,42:19-22.
[11]Iseki K,Tanaka S.Ideal theory of BCK-algebra[J].Mathematica Japonica,1976,2:351-336.
[12]Lei T D,Pu T H.BCK-algebra and BCI-algebra[Z].Lecuture in Shanxi Normal University,1983.
[13]Iseki K.Some properties of BCK-algebras[J].Mathematic Seminar Notes,1974,2:193-201.
[14]Hajek P.Metamathematics of fuzzy logic[M].Kluwer Acad.Publish.,Dordrecht,1998.
[15]Georgescu G,Iorgulescu A.Pseudo-MV algebras:a noncommutative extension of MV algebras[C].The Proceeding of the Fourth International Symposium.on Economic Informatics,Bucharest,Romania,May1999:961-968.
[16]Rachunek J.A non-commutative generalization of MV algebras[J].Czechoslovak Mathematical Joumal,2002,52:255-273.
[17]Rosenfeld A.Fuzzy group[J].Journal Of Mathematical Analysis And Applications,1971,35:512-517.
[18]Dib K A,Galhum N.Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups[J].Fuzzy Sets and Systems,1997,92:103-111.
[19]Mukherjee T K,Sen M K.On fuzzy ideals in ring(I)[J].Fuzzy Sets and Systems,1987,21:99-104.
[20]Chang C L.Fuzzy topological spaces[J].Journal of Mathematical Analysis And Applications,1968,24:182-190.
[21]彭家寅.Q-代数中具有界限的模糊子代数(英文)[J].内江师范学院学报,2011,26(8):1-5.
[22]Xi O G.Fuzzy BCK-algebras[J].Mathematica Japonica,1991,36(5):935-942.
[23]彭家寅.BCK-代数的(s,t]-模糊子代数与R-模糊代数[J].内江师范学院学报,2015,30(6):1-10.
[24]彭家寅.BCK-代数的Ω-模糊代数理想[J].内江师范学院学报,2008,23(4):5-7.
[25]Dymek G,Walendziak A.Fuzzy ideals of pseudo-BCK algebras[J].Demonstratio Mathematica,2012,XLV(1):1-15.
[26]Jun Y B.Fuzzy pseudo-ideals of pseudo-BCK algebras[J].Journal of Applied Mathematics and Computing,2003,12(1):243-250.
[27]彭家寅.直觉模糊BCK-代数[J].淮阴师范学院学报,2011,10(4):296-303.
[28]彭家寅.Vague B-代数(英文)[J].内江师范学院学报,2012,27(4):1-5.
[29]Yamak S,Kazanci O,Davvaz B.Applications of interval-valued t-norms(t-conorms)to fuzzy n-ary sub-hypergroups[J].Information Sciences,2008,178:3957-3972.
[30]彭家寅.区间值(∈,∈∨q)-模糊B-代数(英文)[J].内江师范学院学报,2012,27(2):1-4.
[31]彭家寅.LA-半群中的区间值(∈,∈∨q)-模糊理想[J].内江师范学院学报,2015,30(10):1-9.
[32]彭家寅.LA-半群中的区间值-模糊理想(英文)[J].内江师范学院学报,2015,30(8):1-10.
[33]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.