基于Lukasiewicz的直觉模糊三I蕴涵算子R_(IL)  

Intuitionistic fuzzy triple I implication operator R_(IL) based on Lukasiewicz implication

作　　者：薛占熬[1] 刘杰[1] 程慧茹[2] 王朋函 

机构地区：[1]河南师范大学计算机与信息工程学院,新乡453007 [2]河南师范大学数学与信息科学学院,新乡453007

出　　处：《南京大学学报（自然科学版）》2015年第1期99-104,共6页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(61273018);河南省基础与前沿技术研究计划(132300410174);河南省教育厅计划(14A520082)

摘　　要：全蕴涵三I算法是一种重要的模糊推理算法,其蕴涵采用的是R0蕴涵算子.在直觉模糊集理论基础上,结合三I方法和Lukasiewicz蕴涵算子的概念,构造出一种新的直觉模糊三I蕴涵算子RIL,并运用RIL对直觉模糊取式(IFMP)问题进行求解,得到了基于RIL的IFMP问题求解的算法,同时还证明了直觉模糊蕴涵三IIFMP算法的还原性.Zadeh＇s CRI method is wildly applied in fuzzy reasoning,but it has been criticised to be too complex and it has no reducibility.To alleviate CRI method＇s drawback,the method of triple I was proposed by Wang,which is widely recognized as one of the important fuzzy reasoning methods,and many existing fuzzy inference methods are based on it.In recent years,the triple I method is successfully used in various research fields.The implication operator of R0 is adopted in the triple I method,while some researchers proposed the triple I methods based on other implication operators,such as RL,RGand RGR.All those implication operators were applied in the fuzzy sets successfully.However,triple Iimplication operators based on intuitionistic fuzzy sets have been seldom studied.In this paper,an implication operator based on intuitionistic fuzzy sets was constructed and its properties were studied in detail.Firstly,we reviewed the concepts and related properties of the triple I method and intuitionistic fuzzy sets.At the same time,the definition of the intuitionistic fuzzy triple implication was explained again.Secondly,in the view of implication operator R0 in the intuitionistic fuzzy triple implication,combining the implication operator RL,a new triple Iimplication operator RILin intuitionistic fuzzy sets were presented in this paper.Namely,on the intuitionist fuzzy triple implication,the operator R0 was replaced by the new implication operator RIL.The membership and non-mem-bership functions of RILin intuitionistic fuzzy sets were defined,respectively.Based on the solution method of the intuitionistic fuzzy triple implication,the algorithm by using implication operator RILto solve intuitionistic fuzzy modus ponens problem was performed,then a concrete proof process was provided in detail,which can verify its accuracy.Meanwhile,the reversibility of this algorithm was proved.Thirdly,this paper has a try in proposing a new reasoning of full implication based on intuitive fuzzy logic,and developing the theory of fuzzy reasoni

关 键 词：直觉模糊集 三I方法 直觉模糊三I蕴涵 蕴涵算子 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]