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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (5): 88-98.doi: 10.6040/j.issn.1671-9352.0.2018.386

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否定非对合剩余格的双极值模糊理想

刘春辉,李玉毛,张海燕   

  1. 赤峰学院数学与统计学院, 内蒙古 赤峰 024001
  • 发布日期:2019-05-09
  • 作者简介:刘春辉(1982— ), 男, 硕士, 副教授, 研究方向为非经典数理逻辑与拓扑学. E-mail:chunhuiliu1982@163.com
  • 基金资助:
    内蒙古自治区高等学校科学研究项目(NJZY18206)

Bipolar fuzzy ideals in negative non-involutive residuated lattices

LIU Chun-hui, LI Yu-mao, ZHANG Hai-yan   

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Published:2019-05-09

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摘要： 基于双极值模糊集理论研究否定非对合剩余格的理想问题。首先,引入否定非对合剩余格的双极值模糊理想概念并讨论其基本性质和等价刻画。其次,借助于双极值模糊集的正t-截集和负s-截集等概念考察了双极值模糊理想与理想的关系。最后,在一个否定非对合剩余格的全体双极值模糊理想之集上构造等价关系,并获得了相应的商集性质。

关键词: 模糊逻辑, 逻辑代数, 否定非对合剩余格, 理想, 双极值模糊理想

Abstract: Based on the theory of bipolar fuzzy sets, the problem of ideals in negative non-involutive residuated lattices is studied. Firstly, the concept of bipolar fuzzy ideals in negative non-involutive residuated lattices is introduced, and some their basic properties and equivalent characterizations are discussed. Secondly, the relationships between bipolar fuzzy ideals and ideals are investigated by using the concepts of positive t-cut and negative s-cut set of bipolar valued fuzzy sets. Finally, some equivalence relations are constructed on the set of all bipolar fuzzy ideals in a negative non-involutive residuated lattice, and the properties of corresponding quotient sets are obtained. It further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.

Key words: fuzzy logic, logical algebra, negative non-involutive residuated lattice, ideal, bipolar fuzzy ideal

中图分类号: 

  • O141.1
[1] 王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社, 2003. WANG Guojun. Nonclassical mathematical logic and approximate reasoning[M]. Beijing: Science Press, 2003.
[2] WARD M, DILWORTH R P. Residuated lattices[J]. Transactions of the American Mathematical Society, 1939, 45:335-354.
[3] PAVELKA J. On fuzzy logic Ⅰ, Ⅱ, Ⅲ[J]. Zeitschrift F Math Logic and Grundlagend Math, 1979, 25(1):45-52; 25(2):119-134; 25(5):447-464.
[4] WANG Guojun, ZHOU Hongjun. Introduction to mathematical logic and resolution principle[M]. 2nd ed. Beijing: Science Press, 2009.
[5] HÁJEK P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[6] XU Yang, RUAN D, QIN Keyun, et al. Lattice-valued logics[M]. Berlin: Springer, 2003.
[7] 裴道武. MTL代数的特征定理[J]. 数学学报, 2007, 50(6):1201-1206. PEI Daowu. The characterizations of MTL algebras[J]. Acta Mathematica Sincia, 2007, 50(6):1201-1206.
[8] TURUNEN E. Boolean deductive systems of BL-algebras[J]. Arch Math Logic, 2001, 40(6):467-473.
[9] MICHIRO K, WIESLAW A D. Filter theory of BL-algebras[J]. Soft Computing, 2008, 12(5):419-423.
[10] ZHU Yiquan, XU Yang. On filter theory of residuated lattices[J]. Information Sciences, 2010, 180(16):3614-3632.
[11] DUMITRU B, DANA P. Some types of filters on residuated lattices[J]. Soft Computing, 2014, 18(5):825-837.
[12] LIU Yonglin, LIU Sanyang, XU Yang, et al. ILI-ideals and prime LI-ideals in lattice implication algebras[J]. Information Sciences, 2003, 155(1/2):157-175.
[13] 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. LIU Chunhui. Theory of filters in Fuzzy implication algebras[J]. Journal of Shandong University(Natural Science), 2013, 48(9):73-77.
[14] LELE C, NGANOU J B. MV-algebras derived from ideals in BL-algebras[J]. Fuzzy Sets and Systems, 2013, 218(4):103-113.
[15] LIU Yi, QIN Yao, QIN Xiaoyan, et al. Ideals and fuzzy ideals on residuated lattices[J]. International Journal of Machine Learning and Cybernetics, 2017, 8(1):239-253.
[16] 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. LIU Chunhui. LI-ideals theory in negative non-involutive residuated lattices[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4):445-456.
[17] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[18] ZHANG W R. Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis[C] // Proceedings of the First International Joint Conference of the North American Fuzzy Information Processing Society Biannual Conference, Berlin: Springer, 1994: 305-309.
[19] ZHANG W R. Yin Yang bipolar relativity: a unifying theory of nature, agents and causality wihth applications in quantum computing, cogintive informatics and lift sciences[M]. US: IGI Global, 2011.
[20] LEE K M. Bipolar-valued fuzzy sets and their operations[C] // Proceedings of International Conference on Intelligent Technologies, Bangkok Thailand: Springer, 2000: 307-312.
[21] AKRAM M. Bipolar fuzzy graphs[J]. Information Sciences, 2011, 181(24):5548-5564.
[22] SAEID A B, RAFSANJANI M K. Some results in bipolar-valued fuzzy BCK/BCI-algebras[C] // Proceedings of International Conference on Networked Digital Technologies, Prague, Czech Republic: Springer, 2010: 163-168.
[23] MAJUNDER S K. Bipolar-valued fuzzy in Γ-semigroups[J]. Mathematica Aeterna, 2012, 2(3):203-213.
[24] MAHMOOD K, HAYAT K. Characterizations of Hemi-rings by their bipolar-valued fuzzy h-ideals[J]. Information Sciences Letters, 2015, 4(2):51-59.
[25] JANA C, PAL M, SAEID A B.(∈,∈∨q)-bipolar-valued fuzzy BCK/BCI-algebras[J]. Missouri Journal of Mathematical Sciences, 2017, 29(5):101-112.
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