模糊推理的FMT－对称I*算法

南京大学学报(自然科学版) ›› 2018, Vol. 54 ›› Issue (4): 706–.

模糊推理的FMT－对称I*算法

唐益明1，2*，张有成1，2，任福继1，2，胡相慧1，2，宋小成1，2，丰刚永1，2

出版日期:2018-04-30
作者简介:1.合肥工业大学计算机与信息学院，合肥，230601； 2．情感计算与先进智能机器安徽省重点实验室，合肥工业大学，合肥，230601
基金资助:
基金项目：国家自然科学基金(61673156，61432004，U1613217，61672202)，中国博士后科学基金(2014T70585)，安徽省自然科学基金(1408085MKL15，1508085QF129)，国家“八六三”高技术研究发展计划(2012AA011103) 收稿日期：2018－05－11 *通讯联系人，E－mail：tym608@163.com

FMT－symmetric I* method of fuzzy reasoning

Tang Yiming1，2*，Zhang Youcheng1，2，Ren Fuji1，2，Hu Xianghui1，2， Song Xiaocheng1，2，Feng Gangyong1，2

Online:2018-04-30
About author:1.School of Computer and Information，Hefei University of Technology，Hefei，230601，China； 2．Anhui Province Key Laboratory of Affective Computing and Advanced Intelligent Machine，Hefei University of Technology，Hefei，230601，China

摘要/Abstract

摘要： 面向模糊推理的FMT(Fuzzy Modus Tollens)问题，从对称蕴涵的角度，将三I*算法推广为对称I*算法. 首先，给出了FMT－对称I*算法的定义、求解原则，针对R－蕴涵算子构建了一致化表达的求解模式；针对几个常见的R－蕴涵算子，提供了具体的优化解形式. 进一步地，将FMT－对称I*算法衍生到α－FMT－对称I*算法的范畴，探讨了α－FMT－对称I*算法的定义、求解原理和优化解. 最后，考察了FMT－对称I*算法的置换还原性，发现其效果良好．

Abstract: Fuzzy reasoning plays a significant role in fuzzy control，artificial intelligence，affective computing，image processing，complex system and so forth. The triple I method is currently one of the best methods to deal with the fuzzy reasoning problem. As its improvement，the symmetric implicational method was proposed by us，which contained the triple I* method as its special case. It is well－known that one of the most basic problems of fuzzy reasoning is FMT(Fuzzy Modus Tollens). The purpose of this work is to investigate and analyze the fuzzy reasoning theory of FMT－symmetric I* method，and R－implication operators will also be analyzed. Focusing on the FMT problem of fuzzy reasoning，the triple I* method is generalized to symmetric I* method from the point of view of symmetric implication. First of all，the definition of the FMT－symmetric I* method are proved，then the solving principle of the FMT－symmetric I* method are provided，and the specific form of the FMT－symmetric I* solution is defined. The basic principles of the triple I* method are improved，and uniform expression solutions for R－implication operator are constructed. For several common R－implication operators，specific forms of optimal solutions are provided. Furthermore，the FMT－symmetric I* method is extended to the α－FMT－symmetric I* method. The corresponding definition of the α－FMT－symmetric I* method are discussed. Then the solution principle is further explored. And the optimal solutions of the α－FMT－symmetric I* method is obtained. Finally，the contrapositive reversibility property of the FMT－symmetric I* method is investigated. Reversibility property reflects the compatibility between fuzzy reasoning and classical reasoning，and is an important standard of fuzzy reasoning algorithm，which is often reflected as a basic requirement of fuzzy reasoning algorithm. We analyze the basic FMT－symmetric I* method from the perspective of reversibility property. It is proved that FMT－symmetric I* method has P－permutation reducibility，and it is found that the result of permutation reducibility is excellent.

唐益明1，2*，张有成1，2，任福继1，2，胡相慧1，2，宋小成1，2，丰刚永1，2. 模糊推理的FMT－对称I*算法[J]. 南京大学学报(自然科学版), 2018, 54(4): 706–.

Tang Yiming1，2*，Zhang Youcheng1，2，Ren Fuji1，2，Hu Xianghui1，2， Song Xiaocheng1，2，Feng Gangyong1，2. FMT－symmetric I* method of fuzzy reasoning[J]. Journal of Nanjing University(Natural Sciences), 2018, 54(4): 706–.

参考文献

[1]　Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. 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. 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. 中国科学(E辑)，1999，29(1)：43－53.(Wang G J. Fully implicational triple I method for fuzzy reasoning. Science in China Series E：Technological Sciences，1999，29(1)：43－53.) [4] Wang G J，Fu L. Unified forms of triple I method. Computers & Mathematics with Applications，2005，49(5－6)：923－932. [5] Liu H W. Fully implicational methods for approximate reasoning based on interval－valued fuzzy sets. Journal of Systems Engineering and Electronics，2010，21(2)：224－232. [6] Zhang J C，Yang X Y. Some properties of fuzzy reasoning in propositional fuzzy logic systems. Information Sciences，2010，180(23)：4661－4671.　 [7] Dai S S，Pei D W，Guo D H. Robustness analysis of full implication inference method. International Journal of Approximate Reasoning，2013，54(5)：653－666. [8] Luo M X，Liu B. Robustness of interval－valued fuzzy inference triple I algorithms based on normalized Minkowski distance. Journal of Logical and Algebraic Methods in Programming，2017，86(1)：298－307. [9] 裴道武. FMT问题的两种三I算法及其还原性. 模糊系统与数学，2001，15(4)：1－7.(Pei D W. Two triple I methods for FMT problem and their reductivity. Fuzzy Systems and Mathematics 2001，15(4)：1－7.) [10] Tang Y M，Liu X P. Differently implicational universal triple I method of(1，2，2)type. Computers & Mathematics with Applications，2010，59(6)：1965－1984. [11] Tang Y M，Ren F J. Universal triple I method for fuzzy reasoning and fuzzy controller. Iranian Journal of Fuzzy Systems，2013，10(5)：1－24. [12] Tang Y M，Ren F J. Variable differently implicational algorithm of fuzzy inference. Journal of Intelligent & Fuzzy Systems，2015，28(4)：1885－1897. [13] Tang Y M，Ren F J. Fuzzy systems based on universal triple I method and their response functions. International Journal of Information Technology & Decision Making，2017，16(2)：443－471. [14] Tang Y M，Yang X Z. Symmetric implicational method of fuzzy reasoning. International Journal of Approximate Reasoning，2013，54(8)：1034－1048. [15] Tang Y M，Pedrycz W. On the α(u，v)－symmetric implicational method for R－and(S，N)－implications. International Journal of Approximate Reasoning，2018，92：212－231. [16] Jayaram B，Baczyński M，Mesiar R. R－implications and the exchange principle：The case of border continuous t－norms. Fuzzy Sets and Systems，2013，224：93－105. [17] Liu H W. Fuzzy implications derived from generalized additive generators of representable uninorms. 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. IEEE Transactions on Fuzzy Systems，2007，15(6)：1107－1121. [19] Wang G J，Zhou H J. Introduction to mathematical logic and resolution principle. Beijing：Science Press，2009，335.)

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