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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (8): 20-32.doi: 10.6040/j.issn.1671-9352.0.2018.429

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模糊蕴涵关于合取2-一致模满足输入律的刻画

程亚菲,赵彬*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710119
  • 出版日期:2019-08-20 发布日期:2019-07-03
  • 作者简介:程亚菲(1992— ), 女, 硕士研究生, 研究方向为格上拓扑与非经典数理逻辑. E-mail:chengyafei@snnu.edu.cn*通信作者简介:赵彬(1965— ), 男, 博士, 教授, 博士生导师, 研究方向为格上拓扑与非经典数理逻辑. E-mail:zhaobin@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11531009)

Characterization of fuzzy implications satisfying the law of importation with respect to conjunctive 2-uninorms

CHENG Ya-fei, ZHAO Bin*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

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摘要： 首先引入了模糊否定关于 2-一致模满足(COMPU2)的概念,并讨论了连续的模糊否定分别关于4类合取2-一致模满足(COMPU2)的情形;其次,引入了模糊蕴涵关于合取 2-一致模满足输入律的概念,并给出了其相关性质;最后,利用(COMPU2)给出了模糊蕴涵分别关于4类合取 2-一致模满足输入律的刻画。

关键词: 模糊蕴涵, 2-一致模, 输入律, 模糊否定

Abstract: The notion of fuzzy negations satisfying(COMPU2)with respect to 2-uninorms is introduced, and the situations that continuous fuzzy negations satisfying(COMPU2)with respect to four types of conjunctive 2-uninorms are discussed respectively. The definition and related properties of fuzzy implications satisfying the law of importation with conjunctive 2-uninorms are given. Finally, using(COMPU2), a characterization that fuzzy implications satisfy respectively the law of importation with respect to four types of conjunctive 2-uninorms is provided.

Key words: fuzzy implication, 2-uninorm, the law of importation, fuzzy negation

中图分类号: 

  • O159
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] GOTTWALD S. A treatise on many-valued logics[M]. Baldock: Research Studies Press, 2001.
[3] KERRE E, HUANG C, RUAN D. Fuzzy set theory and approximate reasoning[M]. Wuhan: Wuhan University Press, 2004.
[4] MAS M, MONSERRAT M, TORRENS J, et al. A survey on fuzzy implication functions[J]. IEEE Transactions on Fuzzy Systems, 2007, 15(6):1107-1121.
[5] BUSTINCE H, MOHEDANOA V, BARRENECHEA E, et al. Definition and construction of fuzzy DI-subsethood measures[J]. Information Sciences, 2006, 176(21):3190-3231.
[6] BUSTINCE H, PAGOLA M, BARRENECHEA E. Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images[J]. Information Sciences, 2007, 177(3):906-929.
[7] KERRE E, NACHTEGAEL M. Fuzzy techniques in image processing(studies in fuzziness and soft computing)[M]. New York: Springer, 2000.
[8] YAN P, CHEN G. Discovering a cover set of ARsi with hierarchy from quantitative databases[J]. Information Sciences, 2005, 173(4):319-336.
[9] RADZIKOWSKA A M, KERRE E. A comparative study of fuzzy rough sets[J]. Fuzzy Sets and Systems, 2002, 126(2):137-155.
[10] BACZYNSKI M, JAYARAM B. Fuzzy implication[M]. Berlin: Springer, 2008.
[11] ZADEH L A. Outline of a new approach to the analysis of complex systems and decision processes[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1973, 3(1):28-44.
[12] GONZÁLEZ M, RUIZ-AGUILERA D, TORRENS J. Algebraic properties of fuzzy morphological operators based on uninorms[J]. Artificial Intelligence Research and Development, 2003, 100:27-38.
[13] MASSANET S, TORRENS J. On the characterization of Yagers implications[J]. Information Sciences, 2012, 201:1-18.
[14] MAS M, MONSERRAT M, TORRENS J. A characterization of (U,N), RU, QL and D-implications derived from uninorms satisfying the law of importation[J]. Fuzzy Sets and Systems, 2010, 161(10):1369-1387.
[15] MASSANET S, TORRENS J. The law of importation versus the exchange principle on fuzzy implications[J]. Fuzzy Sets and Systems, 2011, 168(1):47-69.
[16] MASSANET S, TORRENS J. Characterization of fuzzy implication functions with a continuous natural negation satisfying the law of importation with a fixed t-norm[J]. IEEE Transactions on Fuzzy Systems, 2017, 25(1):100-113.
[17] MASSANET S, RUIZ-AGUILERA D, TORRENS J. Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm(Part I)[J]. IEEE Transactions on Fuzzy Systems, 2018, 26(4):1983-1994.
[18] AKELLA P. Structure of n-uninorms[J]. Fuzzy Sets and Systems, 2007, 158(15):1631-1651.
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