您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (08): 22-27.doi: 10.6040/j.issn.1671-9352.1.2014.200

• 论文 • 上一篇    下一篇

面向R-蕴涵算子的FMT-泛三Ⅰ*算法

唐益明, 李小梅, 吴玺   

  1. 合肥工业大学计算机与信息学院, 安徽 合肥 230009
  • 收稿日期:2014-06-02 修回日期:2014-07-08 发布日期:2014-09-24
  • 作者简介:唐益明（1982-），男，博士，讲师，研究方向为模糊理论与应用、情感计算、图像处理.E-mail：tym608@163.com
  • 基金资助:
    国家自然科学基金资助项目（61203077，2014T70585）；中国博士后科学基金资助项目（2012M521218，2014770585）；国家863高技术研究发展计划项目基金（2012AA011103）

FMT-universal triple Ⅰ* method for R-implication operators

TANG Yi-ming, LI Xiao-mei, WU Xi   

  1. School of Computer & Information, Hefei University of Technology, Hefei 230009, Anhui, China
  • Received:2014-06-02 Revised:2014-07-08 Published:2014-09-24

PDF (PC)

645

摘要： 针对模糊推理的FMT（fuzzy modus tollens）问题，作为三Ⅰ*算法的推广与改进形式，研究了FMT-泛三Ⅰ*算法。首先，分析了FMT-泛三Ⅰ*算法的属性，提出了该算法的基本原则，改进了之前三Ⅰ*算法的原则。其次，面向R-蕴涵算子，建立了FMT-泛三Ⅰ*算法的统一形式的解，同时针对几类经典的R-蕴涵算子，分别获得了具体情形下的优化解。最后，证明了FMT-泛三Ⅰ*算法的置换还原性，获得了良好效果。

关键词: 还原性, 模糊推理, 三I算法, 泛三Ⅰ算法

Abstract: Focusing on the FMT(fuzzy modus tollens)problem of fuzzy reasoning, as a generalization and improvement of triple Ⅰ* method, the FMT-universal triple Ⅰ* method is put forward and thoroughly investigated. First of all, the attributes of the FMT-universal triple Ⅰ* method are analyzed, and its basic principle is proposed, which improves the one of triple Ⅰ* method. Furthermore, the unified form of FMT-universal triple Ⅰ* method is established, meanwhile some optimal solutions are obtained for several classical R-implication operators. Finally, the contrapositive reversibility property of FMT-universal triple Ⅰ* method is proved with excellent results.

Key words: fuzzy reasoning, universal triple Ⅰ method, reversibility property, triple Ⅰ method

中图分类号: 

  • O159
[1] 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.
[2] STEPNICKA M, JAYARAM B. On the suitability of the Bandler-Kohout subproduct as an inference mechanism[J]. IEEE Transactions on Fuzzy Systems, 2010, 18(2):285-298.
[3] 王国俊. 模糊推理的全蕴涵三I算法[J]. 中国科学:E辑, 1999, 29(1):43-53. WANG Guojun. Fully implicational triple I method for fuzzy reasoning[J]. Science in China: Series E, 1999, 29 (1):43-53.
[4] WANG Guojun, FU Li. Unified forms of triple I method[J]. Computers & Mathematics with Applications, 2005, 49(5):923-932.
[5] LIU Huawen. Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets[J]. Journal of Systems Engineering and Electronics, 2010, 21(2):224-232.
[6] ZHANG Jiancheng, YANG Xiyang. Some properties of fuzzy reasoning in propositional fuzzy logic systems[J]. Information Sciences, 2010, 180(23):4661-4671.
[7] TANG Yiming, YANG Xuezhi. Symmetric implicational method of fuzzy reasoning[J]. International Journal of Approximate Reasoning, 2013, 54(8):1034-1048.
[8] DAI Songsong, PEI Daowu, GUO Donghui, Robustness analysis of full implication inference method[J]. International Journal of Approximate Reasoning, 2013, 54(5):653-666.
[9] 裴道武. FMT问题的两种三I算法及其还原性[J]. 模糊系统与数学, 2001, 15(4):1-7. PEI Daowu. Two triple I methods for FMT problem and their reductivity[J]. Fuzzy Systems and Mathematics, 2001, 15(4):1-7.
[10] TANG Yiming, LIU Xiaoping. Differently implicational universal triple I method of (1, 2, 2) type[J]. Computers and Mathematics with Applications, 2010, 59(6):1965-1984.
[11] TANG Yiming, REN Fuji, SUN Xiao, et al. Reverse universal triple I method of (1,1,2) type for the Lukasiewicz implication [C]//Proceedings of the 7th Conference on Natural Language Processing and Knowledge Engineering (NLPKE), 2011, Tokushima, 23-30.
[12] TANG Yiming, REN Fuji, CHEN Yanxiang. Differently implicational α-universal triple I restriction method of (1, 2, 2) type[J]. Journal of Systems Engineering and Electronics, 2012, 23(4):560-573.
[13] TANG Yiming, CHEN Yanxiang. Basic universal triple I restriction methods for FMP problem[J]. Applied Mathematics & Information Sciences, 2012, 6(3S):959-966.
[14] 唐益明, 刘晓平. 二值命题逻辑的无损求解[J]. 计算机学报, 2013, 36(5):1097-1114. TANG Yiming, LIU Xiaoping. Lossless solving of two-valued propositional logic[J]. Chinese Journal of Computers, 2013, 36(5):1097-1114.
[15] TANG Yiming, REN Fuji. Universal triple I method for fuzzy reasoning and fuzzy controller[J]. Iranian Journal of Fuzzy Systems, 2013, 10(5):1-24.
[16] JAYARAM B, BACZYŃSKI M, MESIAR R. R-implications and the exchange principle: The case of border continuous t-norms[J]. Fuzzy Sets and Systems, 2013, 224(1):93-105.
[17] LIU Huawen. Fuzzy implications derived from generalized additive generators of representable uninorms[J]. IEEE Transactions on Fuzzy Systems, 2013, 21(3):555-566.
[18] 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.
[19] 王国俊. 数理逻辑引论与归结原理[M]. 2版. 北京: 科学出版社, 2006. WANG Guojun. Introduction to Mathematical Logic and Resolution Principle[M]. 2nd ed. Beijing: Science in China Press, 2006.
[1] 戚方丽, 崔雪莲, 那日萨. 基于在线评论的品牌再购意向模糊推理方法[J]. 山东大学学报（理学版）, 2015, 50(07): 17-22.
[2] 崔雪莲, 洪月, 那日萨. 基于网络评论的消费者重购行为意向挖掘[J]. 山东大学学报（理学版）, 2015, 50(03): 28-31.
[3] 宋 颖,张兴芳,王庆平 . 参数Kleene系统的α-反向三Ⅰ支持算法[J]. J4, 2007, 42(7): 45-48 .
[4] 刘华文,,王国俊,张诚一 . 全蕴涵多Ⅰ算法及其在多准则决策中的应用[J]. J4, 2007, 42(6): 74-80 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发