否定非对合剩余格的IV-模糊理想
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摘要
模糊代数是模糊逻辑的一个重要研究内容。为进一步了解否定非对合剩余格的理想之特性,在否定非对合剩余格中引入了区间值模糊理想概念。讨论了否定非对合剩余格的区间值模糊理想的相关性质。证明了一个否定非对合剩余格的区间值模糊理想的交、直积、同构像和同态原像仍是区间值模糊理想。
Fuzzy algebra is an important content in the study of fuzzy logic. In order to understand the characteristics of ideal in negative non-involutive residuated lattices, the concept of interval valued fuzzy ideal in negative non-involutive residuated lattice is introduced. The related properties of interval valued fuzzy ideal in negative non-involutive residuated lattice are discussed. Furthermore, it is proved that the intersection, direct product, isomorphic image and homomorphism inverse image of interval valued fuzzy ideal in negative non-involutive residuated lattice are also interval valued fuzzy ideals.
Fuzzy algebra is an important content in the study of fuzzy logic. In order to understand the characteristics of ideal in negative non-involutive residuated lattices, the concept of interval valued fuzzy ideal in negative non-involutive residuated lattice is introduced. The related properties of interval valued fuzzy ideal in negative non-involutive residuated lattice are discussed. Furthermore, it is proved that the intersection, direct product, isomorphic image and homomorphism inverse image of interval valued fuzzy ideal in negative non-involutive residuated lattice are also interval valued fuzzy ideals.
引文
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[17]李海霞,吴洪博.R0-代数的Fuzzy子代数与Fuzzy关联MP滤子[J].模糊系统与数学,2008,22(5):22-26.
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[19]刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1):39-45.
[20]Liu Y L,Meng J.Fuzzy ideals in BCI-algebras[J].Fuzzy Sets and Systems,2001,123(2):227-237.
[21]Liu Y,Qin Y,Qin X Y,et al.Ideals and fuzzy ideals on residated lattices[J].International Journal of Machine Learning&Cybernetics,2014,23(5):317-331.
[22]Zadeh L A.The concept of a linguistic variable and its applications to approximate reasoning[J].Information Sciences,1975,8:199-249.
[23]陈露.半群的IV-fuzzy理想[J].纯粹数学与应用数学,2009,25(1):102-106.
[24]刘春辉.R0代数(NM代数)的区间值子代数[J].模糊系统与数学,2012,26(3):77-84.
[25]刘春辉.Fuzzy蕴涵代数的区间值fuzzy滤子[J].计算机工程应用,2010,46(31):39-42.
[2]裴道武.剩余格与正则剩余格的特征[J].数学学报,2002,45(2):271-278.
[3]朱怡权,曹喜望.关于PFI代数与剩余格[J].数学进展,2006,35(2):223-231.
[4]刘春辉,徐罗山.关于剩余格的理想[J].山东大学学报:理学版,2010,45(4):66-71.
[5]任兰,张小红.幂等剩余格[J].模糊系统与数学,2011,25(3):21-29.
[6]梁聪,张小红.预线性与对合非结合剩余格[J].模糊系统与数学,2012,26(3):17-23.
[7]方进明.剩余格与模糊集[M].北京:科学出版社,2012.
[8]刘春辉.否定非对合剩余格的LI-理想理论[J].高校应用数学学报:A辑,2015,30(4):445-456.
[9]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338-353.
[10]Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971(35):512-517.
[11]Jun Y B,Ahn S S,Kim H S.Fuzzy subinclines(ideals)of incline algebras[J].Fuzzy Sets and Systems,2001,123(2):217-225.
[12]刘春辉.MTL代数的模糊理想[J].浙江大学学报:理学版,2015,42(5):514-520.
[13]刘春辉.有界Heyting代数的LI模糊理想格[J].工程数学学报,2016,33(4):391-401.
[14]Liu L Z,Li K T.Fuzzy filters of BL-algebras[J].Information Sciences,2005,173(1/3):141-154.
[15]刘春辉.格蕴涵代数的素模糊LI理想及其谱空间[J].高校应用数学学报:A辑,2014,29(1):115-126.
[16]Peng Jiayin.(∈,∈∨q)-fuzzy LI-ideals in lattice implication algebras[J].Lecture Notes in Electrical Engineering,2012,135:221-226.
[17]李海霞,吴洪博.R0-代数的Fuzzy子代数与Fuzzy关联MP滤子[J].模糊系统与数学,2008,22(5):22-26.
[18]Zhan J M,Davvaz B,Jun Y B.Generalized fuzzy algebraic hypersystems[J].Italian Journal of Pure&Applied Mathematics,2013,30:43-58.
[19]刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1):39-45.
[20]Liu Y L,Meng J.Fuzzy ideals in BCI-algebras[J].Fuzzy Sets and Systems,2001,123(2):227-237.
[21]Liu Y,Qin Y,Qin X Y,et al.Ideals and fuzzy ideals on residated lattices[J].International Journal of Machine Learning&Cybernetics,2014,23(5):317-331.
[22]Zadeh L A.The concept of a linguistic variable and its applications to approximate reasoning[J].Information Sciences,1975,8:199-249.
[23]陈露.半群的IV-fuzzy理想[J].纯粹数学与应用数学,2009,25(1):102-106.
[24]刘春辉.R0代数(NM代数)的区间值子代数[J].模糊系统与数学,2012,26(3):77-84.
[25]刘春辉.Fuzzy蕴涵代数的区间值fuzzy滤子[J].计算机工程应用,2010,46(31):39-42.