BE-代数的犹豫模糊滤子和犹豫模糊同余关系
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摘要
运用犹豫模糊集的方法和原理研究BE-代数的滤子和同余关系问题.首先,引入了BE-代数的犹豫模糊滤子概念,获得了犹豫模糊滤子的若干性质和等价刻画.其次,引入了BE-代数的犹豫模糊同余关系概念,讨论了犹豫模糊同余关系的性质及其与犹豫模糊滤子概念之间的关系,给出了BE-代数在给定犹豫模糊同余关系下的商代数特征并建立了同态基本定理.
Applying the method and principle of hesitant fuzzy sets, the problems of filter and congruence relation are studied. Firstly, the notion of hesitant fuzzy filters is introduced in BE-algebras. Some their properties and equivalent characterizations are obtained. Secondly, the concept of hesitant fuzzy congruence relations is introduced in BE-algebras, the properties of them and their relationship with the notion of hesitant fuzzy filters are discussed. The quotient algebra feature of an BE-algebra under a given hesitant fuzzy congruence relation is given, and the homomorphism fundamental theorem is established.
Applying the method and principle of hesitant fuzzy sets, the problems of filter and congruence relation are studied. Firstly, the notion of hesitant fuzzy filters is introduced in BE-algebras. Some their properties and equivalent characterizations are obtained. Secondly, the concept of hesitant fuzzy congruence relations is introduced in BE-algebras, the properties of them and their relationship with the notion of hesitant fuzzy filters are discussed. The quotient algebra feature of an BE-algebra under a given hesitant fuzzy congruence relation is given, and the homomorphism fundamental theorem is established.
引文
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[4] GOGUEN J A.L-fuzzy sets[J].J Math Anal Appl,1967,18(1):145-174.
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[9] TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[10] VERMA R,SHARMA B D.New operations over hesitant fuzzy sets[J].Fuzzy Information and Engineering,2013,5(2):129-146.
[11] WEI Guiwu.Hesitant fuzzy prioritized operations and their application to multiple attribute decision making[J].Knowledge-Based Systems,2012,31:176-182.
[12] XIA Meimei,XU Zeshui.Hesitant fuzzy information aggregation in decision making[J].International Journal Approx.Reasoning,2011,52(3):395-407.
[13] XU Zeshui,XIA Meimei.Distance and similarity measures for hesitant fuzzy sets[J].Informations Sciences,2011,181(11):2128-2138.
[14] XU Zeshui.Hesitant fuzzy sets theory[M].New York:Springer,2013.
[15] JUN Y B,SUN S A.Hesitant fuzzy set theory applied to BCK/BCI-algebras[J].J Computational Analysis and Applications,2016,20(4):635-646.
[16] KIM H S,KIM Y H.On BE-algebras[J].Science Math Jpn,2007,66(1):113-116.
[17] MENG Biaolong.On filters in BE-algebras[J].Science Math Jpn,2010,71(2):201-207.
[18] WALENDZIAK A.On normal filters and congruence relations in BE-algebras[J].Commentationes Math,2012,52(2):199-205.
[19] RAO S M.Fuzzy implicative filters of BE-algebras[J].Annals of Fuzzy Mathematics and Information,2013,6(3):755-765.
[2] ATANASSOV K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[3] MIZUMOTO M,TANAKA K.Some properties of fuzzy sets of type 2[J].Information Control,1976,31(4):312-340.
[4] GOGUEN J A.L-fuzzy sets[J].J Math Anal Appl,1967,18(1):145-174.
[5] ZADEH L A.The concept of a linguistic variable and its application to approximate reason[J].Information Sciences,1975,8(3):199-249.
[6] GAU W L,BUEHRER D J.Vague sets[J].IEEE Transactions on Systems,Man and Cybernetics,19993,23(20):610-614.
[7] MIYAMOTO S.Multisets and fuzzy multisets[A]//Soft computing and human-centered machines,LIU Zhiqiang,MIYAMOTO S.Tokyo:Springer,2000:9-33.
[8] TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]//The 18th IEEE International Conference on Fuzzy Systems,2009:1378-1382.
[9] TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[10] VERMA R,SHARMA B D.New operations over hesitant fuzzy sets[J].Fuzzy Information and Engineering,2013,5(2):129-146.
[11] WEI Guiwu.Hesitant fuzzy prioritized operations and their application to multiple attribute decision making[J].Knowledge-Based Systems,2012,31:176-182.
[12] XIA Meimei,XU Zeshui.Hesitant fuzzy information aggregation in decision making[J].International Journal Approx.Reasoning,2011,52(3):395-407.
[13] XU Zeshui,XIA Meimei.Distance and similarity measures for hesitant fuzzy sets[J].Informations Sciences,2011,181(11):2128-2138.
[14] XU Zeshui.Hesitant fuzzy sets theory[M].New York:Springer,2013.
[15] JUN Y B,SUN S A.Hesitant fuzzy set theory applied to BCK/BCI-algebras[J].J Computational Analysis and Applications,2016,20(4):635-646.
[16] KIM H S,KIM Y H.On BE-algebras[J].Science Math Jpn,2007,66(1):113-116.
[17] MENG Biaolong.On filters in BE-algebras[J].Science Math Jpn,2010,71(2):201-207.
[18] WALENDZIAK A.On normal filters and congruence relations in BE-algebras[J].Commentationes Math,2012,52(2):199-205.
[19] RAO S M.Fuzzy implicative filters of BE-algebras[J].Annals of Fuzzy Mathematics and Information,2013,6(3):755-765.