基于犹豫模糊可信度的知识推理
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摘要
针对不确定性推理中的可信度估值不精确的问题,将犹豫模糊集引入可信度不确定性推理中。提出犹豫模糊可信度的定义,并基于可信度的知识表示给出犹豫模糊可信度的知识表示方式。为解决专家在推理过程中出现的信息缺失问题,提出求解平均值的信息补全方法。构建犹豫模糊可信度的单条规则和多条规则并行关系的运算法则,并给出基于犹豫模糊可信度的知识表示与推理的具体步骤。最后,运用实例验证了所提算法的可行性及有效性。
In order to solve the problem of inaccurate estimation of credibility in uncertainty reasoning,hesitant fuzzy set was introduced into the reasoning of uncertainty in this paper.The concept of hesitant fuzzy credibility was given in this article.On the basis of the knowledge representation based on credibility,the method of knowledge representation of hesitant fuzzy credibility is defined.In order to solve the problem of missing information in the process of reasoning by experts,an information complement method for solving the average value was proposed.A single rule and multiple rules of parallel relationship of the hesitant fuzzy credibility were constructed,and the specific steps of knowledge representation and uncertainty reasoning based on the hesitant fuzzy credibility was given.Finally,an example was given to illustrate the effectiveness and feasibility of the proposed method.
In order to solve the problem of inaccurate estimation of credibility in uncertainty reasoning,hesitant fuzzy set was introduced into the reasoning of uncertainty in this paper.The concept of hesitant fuzzy credibility was given in this article.On the basis of the knowledge representation based on credibility,the method of knowledge representation of hesitant fuzzy credibility is defined.In order to solve the problem of missing information in the process of reasoning by experts,an information complement method for solving the average value was proposed.A single rule and multiple rules of parallel relationship of the hesitant fuzzy credibility were constructed,and the specific steps of knowledge representation and uncertainty reasoning based on the hesitant fuzzy credibility was given.Finally,an example was given to illustrate the effectiveness and feasibility of the proposed method.
引文
[1]谢季坚,刘承平.模糊数学方法及其应用(第4版)[M].武汉:华中科技大学出版社,2013.
[2]刘星成,汤庸.专家系统原理与编程[M].北京:机械工业出版社,2000.
[3]SHORTILIFFE E H.Computer-based medical consultation:MYCIN[M].New York:American Elsevier Publishing,1976.
[4]HAO Q,LU T.Context modeling and reasoning based on certainty factor[C]∥Proceedings of 2009Second Asia-Pacific Conference on Computational Intelligence and Industrial Applications.Wuhan,China:IEEE,2009:38-41.
[5]WU M K.The truth-value estimation in fuzzy reasoning[J].Chinese Journal of Computers,1993,16(2):158-161.(in Chinese)吴茂康.关于Fuzzy推理式的可信度估计[J].计算机学报,1993,16(2):158-161.
[6]CHEN Y X,YIN Y.Two kinds of reasoning with credibility[J].Fuzzy Systems and Mathematics,2005,19(3):6-13.(in Chinese)陈仪香,尹艳.两种含可信度的推理[J].模糊系统与数学,2005,19(3):6-13.
[7]XIONG C Q,OUYANG Y,MEI Q.Argumentation Model Based on Certainty-Factor and Algorithms of Argument Evaluation[J].Journal of Software,2014,25(6):1225-1238.(in Chinese)熊才权,欧阳勇,梅清.基于可信度的辩论模型及争议评价算法[J].软件学报,2014,25(6):1225-1238.
[8]ZOU L,ZHANG Y X,LIU X.Linguistic-Valued approximate reasoning with lattice ordered linguistic-valued credibility[J].International Journal of Computational Intelligence Systems,2015,8(1):53-61.
[9]ZADEH L A.The concept of a linguistic variable and its applications to approximate reasoning-Part I[J].Information Science,1975,8(3):199-249.
[10]FAN J P,XUE K,WU M Q.Cross evaluation method based on intuitionistic fuzzy entropy[J].Computer Science,2018,45(2):280-286.(in Chinese)范建平,薛坤,吴美琴.基于直觉模糊熵的交叉评价方法[J].计算机科学,2018,45(2):280-286.
[11]YAGER R R,ABBASOV A M.Pythagorean membership grades in multicriteria decision making[J].IEEE Transaction on Fuzzy Systems,2014,22(4):958-965.
[12]TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]∥IEEE International Conference on Fuzzy Systems.IEEE,2009:1378-1382.
[13]TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[14]ZHANG Z.Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency[J].Applied Soft Computing,2016,46:37-59.
[15]PUSHPINDER S.Distance and similarity measures for multipleattribute decision making with dual hesitant fuzzy sets[J].Computational&Applied Mathematics,2015,36(1):1-6.
[16]RODR′IGUEZ R M,MART′INEZ L,HERRERA F.Hesitant Fuzzy Linguistic Term Sets for Decision Making[J].IEEETransactions on Fuzzy Systems,2012,20(1):109-119.
[17]GUO S,JIN F F,CHEN H Y.Hesitant fuzzy Einstein geometric aggregation operators and their application[J].Computer Engineering and Applications,2015,51(17):53-58.(in Chinese)郭甦,金飞飞,陈华友.犹豫模糊Einstein几何算子及应用[J].计算机工程与应用,2015,51(17):53-58.
[18]LIU W F,HE X.Pythagorean Hesitant Fuzzy Set[J].Fuzzy Systems and Mathematics,2016,30(4):107-115.(in Chinese)刘卫锋,何霞.毕达哥拉斯犹豫模糊集[J].模糊系统与数学,2016,30(4):107-115.
[19]XU Z S,ZHANG X L.Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J].Knowledge-Based Systems,2013,52(6):53-64.
[20]LIAO H C,XU Z S,ZENG X J.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(3):125-142.
[21]BIAN S H.Research and application of uncertainty reasoning in expert system[D].Anhui:Anhui University,2010.(in Chinese)卞世晖.专家系统中不确定性推理的研究与应用[D].安徽:安徽大学,2010.
[22]XIA M M,XU Z S,CHEN N.Some hesitant fuzzy aggregation operators with their application in group decision making[J].Group Decis Negot,2013,234(10):259-279.
[23]TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[2]刘星成,汤庸.专家系统原理与编程[M].北京:机械工业出版社,2000.
[3]SHORTILIFFE E H.Computer-based medical consultation:MYCIN[M].New York:American Elsevier Publishing,1976.
[4]HAO Q,LU T.Context modeling and reasoning based on certainty factor[C]∥Proceedings of 2009Second Asia-Pacific Conference on Computational Intelligence and Industrial Applications.Wuhan,China:IEEE,2009:38-41.
[5]WU M K.The truth-value estimation in fuzzy reasoning[J].Chinese Journal of Computers,1993,16(2):158-161.(in Chinese)吴茂康.关于Fuzzy推理式的可信度估计[J].计算机学报,1993,16(2):158-161.
[6]CHEN Y X,YIN Y.Two kinds of reasoning with credibility[J].Fuzzy Systems and Mathematics,2005,19(3):6-13.(in Chinese)陈仪香,尹艳.两种含可信度的推理[J].模糊系统与数学,2005,19(3):6-13.
[7]XIONG C Q,OUYANG Y,MEI Q.Argumentation Model Based on Certainty-Factor and Algorithms of Argument Evaluation[J].Journal of Software,2014,25(6):1225-1238.(in Chinese)熊才权,欧阳勇,梅清.基于可信度的辩论模型及争议评价算法[J].软件学报,2014,25(6):1225-1238.
[8]ZOU L,ZHANG Y X,LIU X.Linguistic-Valued approximate reasoning with lattice ordered linguistic-valued credibility[J].International Journal of Computational Intelligence Systems,2015,8(1):53-61.
[9]ZADEH L A.The concept of a linguistic variable and its applications to approximate reasoning-Part I[J].Information Science,1975,8(3):199-249.
[10]FAN J P,XUE K,WU M Q.Cross evaluation method based on intuitionistic fuzzy entropy[J].Computer Science,2018,45(2):280-286.(in Chinese)范建平,薛坤,吴美琴.基于直觉模糊熵的交叉评价方法[J].计算机科学,2018,45(2):280-286.
[11]YAGER R R,ABBASOV A M.Pythagorean membership grades in multicriteria decision making[J].IEEE Transaction on Fuzzy Systems,2014,22(4):958-965.
[12]TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]∥IEEE International Conference on Fuzzy Systems.IEEE,2009:1378-1382.
[13]TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[14]ZHANG Z.Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency[J].Applied Soft Computing,2016,46:37-59.
[15]PUSHPINDER S.Distance and similarity measures for multipleattribute decision making with dual hesitant fuzzy sets[J].Computational&Applied Mathematics,2015,36(1):1-6.
[16]RODR′IGUEZ R M,MART′INEZ L,HERRERA F.Hesitant Fuzzy Linguistic Term Sets for Decision Making[J].IEEETransactions on Fuzzy Systems,2012,20(1):109-119.
[17]GUO S,JIN F F,CHEN H Y.Hesitant fuzzy Einstein geometric aggregation operators and their application[J].Computer Engineering and Applications,2015,51(17):53-58.(in Chinese)郭甦,金飞飞,陈华友.犹豫模糊Einstein几何算子及应用[J].计算机工程与应用,2015,51(17):53-58.
[18]LIU W F,HE X.Pythagorean Hesitant Fuzzy Set[J].Fuzzy Systems and Mathematics,2016,30(4):107-115.(in Chinese)刘卫锋,何霞.毕达哥拉斯犹豫模糊集[J].模糊系统与数学,2016,30(4):107-115.
[19]XU Z S,ZHANG X L.Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J].Knowledge-Based Systems,2013,52(6):53-64.
[20]LIAO H C,XU Z S,ZENG X J.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(3):125-142.
[21]BIAN S H.Research and application of uncertainty reasoning in expert system[D].Anhui:Anhui University,2010.(in Chinese)卞世晖.专家系统中不确定性推理的研究与应用[D].安徽:安徽大学,2010.
[22]XIA M M,XU Z S,CHEN N.Some hesitant fuzzy aggregation operators with their application in group decision making[J].Group Decis Negot,2013,234(10):259-279.
[23]TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.