否定非对合剩余格的模糊LI理想
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摘要
对否定非对合剩余格的模糊LI理想问题作进一步深入研究.首先,给出了模糊LI理想的一些新性质和新刻画.然后,引入正规模糊LI理想的概念并研究其性质,获得了模糊LI理想成为正规模糊LI理想的若干充要条件.
In this paper, the problem of normal fuzzy LI-ideals in negative non-involutive residuated lattices is further studied. Firstly, some new properties and characterizations of fuzzy LI-ideals are given. Then, the notion of normal fuzzy LI-ideal is introduced its properties are discussed. Some necessary and sufficient conditions for the fuzzy LI-ideal to become a normal fuzzy LI-ideal are obtained.
In this paper, the problem of normal fuzzy LI-ideals in negative non-involutive residuated lattices is further studied. Firstly, some new properties and characterizations of fuzzy LI-ideals are given. Then, the notion of normal fuzzy LI-ideal is introduced its properties are discussed. Some necessary and sufficient conditions for the fuzzy LI-ideal to become a normal fuzzy LI-ideal are obtained.
引文
[1]Ward M, Dilworth R P. Residuated Lattices[J]. Trans Amer Math Soc, 1939, 45:335-354.
[2]Pavelka J. On fuzzy logic I, II, III[J]. Zeitschr F Math Logic and Grundlagend Math, 1979, 25:45-52; 119-134; 447-464.
[3]HáJek P. Metamathematics of Fuzzy Logic[M]. Dordrecht:Kluwer Academic Publishers, 1998.
[4]Wang Guojun, Zhou Hongjun. Introduction to mathematical logic and resolution principle(Second Edition)[M]. Beijing:Science Press, 2009.
[5]刘春辉.Fuzzy蕴涵代数的滤子理论[J].山东大学学报(理学版),2013, 48(9):73-77.
[6]刘春辉.Heyting代数的扩张滤子[J].数学的实践与认识,2017, 47(22):255-261.
[7]Lele C, Nganou J B. MV-algebras derived from ideals in BL-algebras[J]. Fuzzy Sets and Systems,2013, 218:103-113.
[8]Liu Yi, Qin Yao, QIN Xiaoyan, XU Yang. Ideals and fuzzy ideals on residuated lattices[J]. Inter?national Journal of Machine Learning and Cybernetics, 2014:1-15.
[9]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,2015, 30(4):445-456.
[10]Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8:338-353.
[2]Pavelka J. On fuzzy logic I, II, III[J]. Zeitschr F Math Logic and Grundlagend Math, 1979, 25:45-52; 119-134; 447-464.
[3]HáJek P. Metamathematics of Fuzzy Logic[M]. Dordrecht:Kluwer Academic Publishers, 1998.
[4]Wang Guojun, Zhou Hongjun. Introduction to mathematical logic and resolution principle(Second Edition)[M]. Beijing:Science Press, 2009.
[5]刘春辉.Fuzzy蕴涵代数的滤子理论[J].山东大学学报(理学版),2013, 48(9):73-77.
[6]刘春辉.Heyting代数的扩张滤子[J].数学的实践与认识,2017, 47(22):255-261.
[7]Lele C, Nganou J B. MV-algebras derived from ideals in BL-algebras[J]. Fuzzy Sets and Systems,2013, 218:103-113.
[8]Liu Yi, Qin Yao, QIN Xiaoyan, XU Yang. Ideals and fuzzy ideals on residuated lattices[J]. Inter?national Journal of Machine Learning and Cybernetics, 2014:1-15.
[9]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,2015, 30(4):445-456.
[10]Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8:338-353.