计算机科学 ›› 2021, Vol. 48 ›› Issue (11A): 57-62.doi: 10.11896/jsjkx.201200140

• 智能计算 • 上一篇    下一篇

基于公理化模糊集合的模糊推理方法

康波, 潘小东, 王虎   

  1. 西南交通大学数学学院 成都611756
  • 出版日期:2021-11-10 发布日期:2021-11-12
  • 通讯作者: 康波(970269861@qq.com)
  • 基金资助:
    国家自然科学基金(61673320)

Fuzzy Reasoning Method Based on Axiomatic Fuzzy Sets

KANG Bo, PAN Xiao-dong, WANG Hu   

  1. School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Online:2021-11-10 Published:2021-11-12
  • About author:KANG Bo,born in 1995,postgraduate.His main research interests include fuzzy reasoning and so on.
    PAN Xiao-dong,born in 1979,associate professor.His main research interests include mathematical basic theory of fuzzy information processing and so on.
  • Supported by:
    National Natural Science Foundation of China(61673320).

摘要: 以公理化模糊集合理论作为基础,把模糊推理看成两个模糊隶属空间之间的映射,利用输入模糊集合在模糊隶属空间中的构成方式,给出了模糊推理输出结果的3种基本形式。对于强否定算子、t-模算子、t-余模算子,利用Minkowski积分形式的距离讨论了这些算子在模糊隶属空间中的扰动性,并在此基础之上分析所提模糊推理方法的连续性。

关键词: 公理化模糊集合, 模糊推理, 模糊隶属空间, 扰动性, 连续性

Abstract: Based on the axiomatic fuzzy set theory,this paper regards fuzzy reasoning as the mapping between two fuzzy membership spaces,and gives three basic forms of fuzzy reasoning output results by using the composition of input fuzzy sets in fuzzy membership spaces.For strongly negative operators,t-modulus operators and t-comodule operators,the perturbation of these operators in fuzzy membership space is discussed by using Minkowski integral distance,and the continuity of fuzzy reasoning method proposed in this paper is analyzed on this basis.

Key words: Axiomatic fuzzy sets, Fuzzy reasoning, Fuzzy membership space, Perturbation, Continuity

中图分类号: 

  • TP273
[1]ZADEH L A.Fuzzy sets[J].Information & Control,1965,8(3):338-353.
[2]ZADEH L A.Outline of a new approach to the analysis of complex systems and decision processes.[J].IEEETransactions on Systems Man and Cybernetics,1973,3(1):28-44.
[3]LI H X.Interpolation mechanism of fuzzy control[J].Science in China(Series E),1998,28(3):259-267.
[4]WANG Y Y.Logic in computational science[M].Beijing:Science Press,1989.
[5]ANTONIOU G.Nonmonotonic reasoning[M].Cambridge:MIT Press,1997.
[6]WANG G J.Non-classical mathematical logic and approximatereasoning[M].Beijing:Science Press,2008.
[7]SONG S J,WU C.Inverse triple I algorithm for fuzzy reasoning[J].Chinese Science(Series E),2002,32(2):230-135.
[8]ZOU X F,PEI D W.SIS algorithms of fuzzy reasoning[J].Fuzzy System and Mathematics,2010,24(6):1-7.
[9]ZHEN M Q,SHI Z K,LIU Y.Triple I method of intuitionistic fuzzy reasoning based on residual implicator[J].Science in China,2013,43(6):810-820.
[10]TANG Y M,ZHANG Y C,RENF J,et al.FMT- symmetric I* method for fuzzy reasoning[J].Journal of Nanjing University (Natural Sciences),2018,54(4):706-713.
[11]PENG J Y.Reverse Triple I Method of Intuitionistic Fuzzy Reasoning Based on Residual Implicator[J].PatternRecognition and Artificial Intelligence,2018,31(6):525-536.
[12]PENG J Y.Full implication method of interval-valued intuitionis-tic fuzzy reasoning[J].Fuzzy Systems and Mathematics,2019,33(3):35-45.
[13]PAN X D,XU Y.Redefinition of the concept of fuzzy set based on vague partition from the perspective of axiomatization[J].Soft Computing A Fusion of Foundations Methodologies & Applications,2018,22:1777-1789.
[14]PAN X D,XU Y.Correction to:Redefinition of the concept of fuzzy set based on vague partition from the perspective of axiomatization[J].Soft Computing,2018,22(6):2079-2079.
[15]MARTIN Š,ULRICH B,MARTINA D,et al.Continuity issues of the implicational interpretation of fuzzy rules[J].Fuzzy Sets Systems,2010,161(14):1959-1972.
[16]LIU H W,WANG G J,Continuity of triple I methods based on several implications[J].Comput.Math.Appl.,2008,56:2079-2087.
[17]JENEI S.Continuity in Zadeh's compositional rule of inference[J].Fuzzy Sets and Systems,1999,104(2):333-339.
[18]LUO M X,YAO N.Triple I algorithms based on Schweizer-Sklar operators in fuzzy reasoning[J]Int.J.Approx.Reason.,2013,54:640-652.
[19]DAI S S,PEI D W,WANG S M.Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distance[J].Fuzzy Sets Systems,2012,189:63-73.
[20]HU B Q.Fuzzy theoretical basis[M].Wuhan:Wuhan University Press,2008.
[21]HONG D H,WANG S Y.A note on the value similarity of fuzzy systems variables[J].Fuzzy Sets and Systems,1994,66(3):383-386.
[22]RUDIN W.Real and Complex Analysis[M].Beijing:China Machine Press,2006:61-64.
[1] 祝轩, 王磊, 张超, 梅东锋, 薛珈萍, 曹晴雯. 基于连续性约束背景模型减除的运动目标检测[J]. 计算机科学, 2019, 46(6): 311-315.
[2] 薛彬彬,秦克云. 基于模糊软集的三I推理方法的性质[J]. 计算机科学, 2018, 45(5): 215-219.
[3] 邢瑞康, 李成海. 基于直觉模糊集理论的IDS方法研究[J]. 计算机科学, 2018, 45(11A): 344-348.
[4] 吴志军,刘中,胡涛涛. 面向SWIM系统改进的服务调度算法[J]. 计算机科学, 2017, 44(Z11): 366-371.
[5] 徐本强,谭雪微,邹丽. 基于真值支持度的直觉模糊推理方法[J]. 计算机科学, 2016, 43(3): 68-71.
[6] 张新菊,姚淑珍. 基于模糊着色Petri网的多状态系统可靠性分析[J]. 计算机科学, 2016, 43(11): 77-82.
[7] 吴晓刚,潘正华. 基于模糊命题逻辑形式系统FLcom的模糊推理及应用[J]. 计算机科学, 2015, 42(Z11): 100-103.
[8] 吴少群 袁红星 安 鹏 程培红. 图像引导的二阶总广义变分稀疏深度图的稠密重构[J]. 计算机科学, 2015, 42(7): 314-319.
[9] 王万良,石浩,李燕君. 基于Mamdani型模糊推理的加权质心定位算法[J]. 计算机科学, 2015, 42(10): 101-105.
[10] 朱立新,杨扩,秦加合. 一种新的基于自适应神经网络模糊推理系统的图像滤波器[J]. 计算机科学, 2014, 41(Z6): 211-214.
[11] 任越美,张艳宁,魏巍,张秀伟. 基于稀疏表示和词袋模型的高光谱图像分类[J]. 计算机科学, 2014, 41(10): 113-116.
[12] 施光源,张宇. 基于模糊逻辑的数据分级存储模型研究[J]. 计算机科学, 2013, 40(Z11): 284-287.
[13] 田田,陈勇,刘天甲,赵鑫叶. 军事分析仿真评估系统模糊知识库研究[J]. 计算机科学, 2013, 40(Z11): 153-156.
[14] 罗海驰,李岳阳,孙俊. 一种基于自适应神经模糊推理系统的图像滤波方法[J]. 计算机科学, 2013, 40(7): 302-306.
[15] 窦文阳,王小明,张立臣. 普适计算环境下的安全分布式访问控制系统研究[J]. 计算机科学, 2013, 40(6): 132-137.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 冯芙蓉, 张兆功. 目标轮廓检测技术新进展[J]. 计算机科学, 2021, 48(6A): 1 -9 .
[2] 孙正, 张小雪. 生物光声成像中声反射伪影抑制方法的研究进展[J]. 计算机科学, 2021, 48(6A): 10 -14 .
[3] 周欣, 刘硕迪, 潘薇, 陈媛媛. 自然交通场景中的车辆颜色识别[J]. 计算机科学, 2021, 48(6A): 15 -20 .
[4] 黄雪冰, 魏佳艺, 沈文宇, 凌力. 基于自适应加权重复值滤波和同态滤波的MR图像增强[J]. 计算机科学, 2021, 48(6A): 21 -27 .
[5] 江妍, 马瑜, 梁远哲, 王原, 李光昊, 马鼎. 基于分数阶麻雀搜索优化OTSU肺组织分割算法[J]. 计算机科学, 2021, 48(6A): 28 -32 .
[6] 冯霞, 胡志毅, 刘才华. 跨模态检索研究进展综述[J]. 计算机科学, 2021, 48(8): 13 -23 .
[7] 周文辉, 石敏, 朱登明, 周军. 基于残差注意力网络的地震数据超分辨率方法[J]. 计算机科学, 2021, 48(8): 24 -31 .
[8] 朝乐门, 尹显龙. 人工智能治理理论及系统的现状与趋势[J]. 计算机科学, 2021, 48(9): 1 -8 .
[9] 雷羽潇, 段玉聪. 面向跨模态隐私保护的AI治理法律技术化框架[J]. 计算机科学, 2021, 48(9): 9 -20 .
[10] 王俊, 王修来, 庞威, 赵鸿飞. 面向科技前瞻预测的大数据治理研究[J]. 计算机科学, 2021, 48(9): 36 -42 .