JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (10): 78-94.doi: 10.6040/j.issn.1671-9352.0.2016.123

Previous Articles    

Disturbing fuzzy ideals of BL-algebras

PENG Jia-yin   

  1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641199, Sichuan, China
  • Received:2016-03-25 Online:2016-10-20 Published:2016-10-17

PDF (PC)

706

Abstract: Utilizing the notion of disturbing fuzzy sets, the properties of disturbing fuzzy ideals of BL-algebras are investigated. The concept of disturbing fuzzy ideal is introduced and its several properties are studied. A quotient BL-algebra via a disturbing fuzzy ideal is constructed, and the disturbing fuzzy homomorphism fundamental theorem is given. Moreover, a procedure to generate a disturbing fuzzy ideal is given by a disturbing fuzzy set. Some classes of disturbing fuzzy ideals are defined and the relations of them are investigated. Some characterizations of disturbing fuzzy Boolean ideals, disturbing fuzzy prime ideals, disturbing fuzzy irreducible ideals, disturbing fuzzy ultra ideals, disturbing fuzzy Godel ideals are established.

Key words: disturbing fuzzy ultra ideal, disturbing fuzzy obstinate ideal, disturbing fuzzy ideal, disturbing fuzzy irreducible ideal, disturbing fuzzy Godel ideal, disturbing fuzzy Boolean ideal, BL-algebra, disturbing fuzzy prime ideal

CLC Number: 

  • O159
[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. WANG Yuanyuan. Modern logic in computer science[M]. Beijing: Science and Technology Press, 2001: 207.
[6] LIN T L. A set theory for soft computing[C]. Proceeding of 1996 IEEE International Con-ference on Fuzzy Systems, 1996: 1140-1146.
[7] YING Mingsheng. 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. LIU Xin, CHEN Tuyun. Disturbing fuzzy logic and its “negation operater”[J]. Fuzzy Systems and Mathematic, 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] HAJK P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[11] 邵晓丽,吴洪博. 次BL代数的修正及应用[J]. 太原师范学院学报(自然科学版),2006, 5(4):1-4. SHAO Xiaoli, WU Hongbo. Correction and application of su-BL algebra[J]. Journal of Taiyuan Normal University(Natural Science Edition), 2006, 5(4):1-4.
[12] 朱翔,徐罗山. BL代数的等价刻画及更多性质[J]. 模糊系统与数学,2011, 25(1):13-18. ZHU Xiang, XU Luoshan. The equivalent characterization and more properities of BL algebras[J]. Fuzzy Systems and Mathematic, 2011, 25(1):13-18.
[13] 杨永伟,辛小龙. 特殊BL-代数的进一步的研究[J]. 模糊系统与数学,2015, 29(2):54-61. YANG Yongwei, XIN Xiaolong. Further research on special BL algebras[J]. Fuzzy Systems and Mathematic, 2015, 29(2):54-61.
[14] 冯敏. BL代数和MV代数上的导子理论[D]. 陕西:西北大学,2015. FENG Min. Derivation theory of BL algebras and MV algebras[D]. Shaanxi: Northwestern University, 2015.
[15] TURUNEN E. Boolean deductive systems of BL-agebras[J]. Arch Math Logic, 2001, 40:467-473.
[16] HAVESHKI M, SAEID A B, ESLAMI E. Some types of filters in BL algebras[J]. Soft Computing, 2006, 10(8):657-664.
[17] SAEID A B, MOTAMED S. Normal filters in BL-algebras[J]. World Applied Sciences Journal, 2009, 7:70-76.
[18] 王伟,杨廉,石召,等. BL-代数的fantastic滤子和normal滤子[J]. 纯粹数学与应用数学,2012, 28(5):595-598. WANG Wei, YANG Lian, SHI Zhao, et al. Fantastic filter and normal filter of BL algebras[J]. Pure Mathematics and Appled Mathematics, 2012, 28(5):595-598.
[19] 杨永伟,贺鹏飞,李毅君. BL-代数的严格滤子[J]. 山东大学学报(理学版),2014, 49(3):63-67. YANG Yongwei, HE Pengfei, LI Yijun. Strict filter of BL algebras[J]. Journal of Shandong University(Natural Science), 2014, 49(3):63-67.
[20] 王伟,李毅君,童丹,等. BL-代数的obstinate滤子和ultra滤子[J]. 内蒙古师范大学学报(自然科学汉文版),2013, 42(4):380-382. WANG Wei, LI Yijun, TONG Dan, et al. Obstinte filter and ultra filter of BL algebras[J]. Journal of Inner Mongolia Normal University(Natural Science Edition), 2013, 42(4):380-382.
[21] SAEID A B, AHADPANAH A, TORKZADEH L. Smarandache BL-algebras[J]. Journal of Applied Logic, 2010, 8(3):253-261.
[22] LIU Lianzhen, LI Kaitai. Fuzzy filters of BL-algebras[J]. Information Sciences, 2005, 173(1-3):141-154.
[23] LIU Lianzhen, LI Kaitai. Fuzzy Boolean and positive implicative filters of BL-algebras[J]. Fuzzy Sets and Systems, 2005, 152(2):333-348.
[24] ZHAN Jianming, XU Yang. Some types of generalized fuzzy filiters of BL-algebras[J]. Computers and Mathematics, 2008, 56(6):1604-1616.
[25] JUN Y B, CHO Y U, ROH E H, et al. General types of(∈,∈∨q)-fuzzy filiters in BL-algebras[J]. Neural Computing and Applications, 2011, 20(3):355-343.
[26] 刘春辉. BL代数的(∈,∈∨q)-模糊滤子理论[J]. 模糊系统与数学,2015, 29(1):50-58. LIU Chunhui.(∈,∈∨q)-fuzzy filter theory of BL algebras[J]. Fuzzy Systems and Mathematic, 2015, 29(1):50-58.
[27] 彭家寅.BL-代数中(∈,∈∨q)-模糊蕴滤子的重数[J]. 内江师范学院学报,2014, 29(12):1-8. PENG Jiayin. Foldness of(∈,∈∨q)-fuzzy implicative filters in BL-algebras[J]. Journal of Neijiang Normal University, 2014, 29(12):1-8.
[28] 孟彪龙,辛小龙,杨永伟. BL-代数的n-重模糊蕴涵滤子[J]. 计算机工程与应用,2014, 50(11):62-65. MENG Biaolong, XIN Xiaolong, YANG Yongwei. The n-folds fuzzy implicative filter of BL-algebras[J]. Computer Engineering and Application, 2014, 50(11):62-65.
[29] ZHANG Xiaohong, JUN Young Bae, DOH Myung Im. On fuzzy filiters and fuzzy ideals of BL-algebras[J]. Fuzzy Systems and Mathematic, 2006, 20(3):8-20.
[30] LELE C, NGANOU J B. MV-algebras derived form in BL-algebras[J]. Fuzzy Sets and Systems, 2013, 218:103-113.
[31] MENG Biaolong, XIN Xiaolong. On fuzzy ideals of BL-algebars[OL]. Hindawi Publishing Corporation, The Scientific Word Journal. http://dx.doi.org/10.1155/2014/757382.
[32] 杨永伟,贺鹏飞,李毅君. BL-代数中的落影模糊理想[J]. 山东大学学报(理学版),2015, 50(2):83-89. YANG Yongwei, HE Pengfei, LI Yijun. Fall shadow fuzzy ideals of BL algebras[J]. Journal of Shandong University(Natural Science), 2015, 50(2):83-89.
[33] LELE C, NGANOU J B. Pseudo-addition and fuzzy ideal in BL-algebras[J]. Annals of Fuzzy Mathematic and Informatics, 2014, 8(2):193-207.
[34] 孟彪龙. BL-代数的理想/滤子专题研究[D]. 陕西:西北大学,2015. MENG Biaolong. Specail subject research on ideals/filters of BL algebras[D]. Shaanxi: Northwestern University, 2015.
[35] YANG Yongwei, XIN Xiaolong, HE Pengfei.(∈γ, ∈γ, ∨qδ)-intuitionistic fuzzy(soft)filter of BCK-algebras[J]. Chin Quart J of Math, 2014, 29(1):65-75.
[36] 薛占熬,肖运花,薛天宇,等. BL-代数上的几种直觉模糊滤子[J]. 计算机科学,2012,39(9):197-219. XUE Zhanao, XIAO Yunhua, XUE Tianyu, et al. Several intuitionistic fuzzy filters of BL algebras[J]. Computer Science, 2012, 39(9):197-219.
[37] PENG Jiayin. Vague BCK-algebra[C]. 2010 3rd International Conference on Advanced Computer Theory and Engineering Piscataway: IEEI, 2010, 2:271-275.
[38] 刘春辉. BL代数的区间值(∈,∈∨q)-模糊滤子理论[J]. 山东大学学报(理学版),2014,49(10):83-89. LIU Chunhui. Interval valued (∈,∈∨q)-fuzzy filter theory of BL algebras[J]. Journal of Shandong University(Natural Science), 2014, 49(10):83-89.
[39] 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. HAN Ying, CHEN Senfa, CHEN Sheng. The type TD disturbing fuzzy normal subgroups[J]. Fuzzy Systems and Mathematic, 2006, 20(5):25-29.
[40] 韩莹.扰动模糊理论及其在推理决策中的应用[D]. 南京:东南大学,2009: 6-14. HAN Ying. Disturbing fuzzy set theory and its application in reasoning and decision making[J]. Nanjing: Southeast University, 2009: 6-14.
[1] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110.
[2] YANG Yong-wei, HE Peng-fei, LI Yi-jun. Falling fuzzy ideals of BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 83-89.
[3] WEN Xian-hong, WU Hong-bo*. The prime reverse deductive system of locally finite #br# BL-algebras with properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 36-41.
[4] LIU Chun-hui. Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 83-89.
[5] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63-67.
[6] ZHOU Jian-ren, WU Hong-bo*. The regularness of WBR0-algebras and relationship with other logic algebras [J]. J4, 2012, 47(2): 86-92.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd