基于Lukasiewicz的直觉模糊三I 蕴涵算子 R I L

南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (1): 99–104.

基于Lukasiewicz的直觉模糊三I 蕴涵算子 R I L

薛占熬1，刘杰1，程慧茹2，王朋函1

出版日期:2014-12-31 发布日期:2014-12-31
作者简介:(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)
基金资助:
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)

Intuitionistic fuzzy triple I implication operator based on Lukasiewicz implication

Xue Zhan’ao1, Liu Jie1, Cheng Huiru2, Wang Penghan1

Online:2014-12-31 Published:2014-12-31
About author:(1.College of Computer and Information Engineering, Henan Normal University, Xinxiang, 453007, China;
2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China)

摘要/Abstract

摘要： 全蕴涵三I算法是一种重要的模糊推理算法，采用的是蕴含算子。本文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，并运用对直觉模糊取式(IFMP)问题进行求解，得到了基于的IFMP问题求解的算法，同时还证明了直觉模糊蕴涵三I IFMP算法的还原性。

Abstract: Zadeh’s CRI method is wildly applied in fuzzy reasoning, but it has been criticized 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 is adopted in the triple I method, while some researchers proposed the triple I methods based on other implication operators, such as , and . All those implication operators were applied in the fuzzy sets successfully. However, triple I implication 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 in the intuitionistic fuzzy triple implication, combining the implication operator , a new triple I implication operator in intuitionistic fuzzy sets were presented in this paper. Namely, on the intuitionist fuzzy triple implication, the operator was replaced by the new implication operator . The membership and non-membership functions of in intuitionistic fuzzy sets were defined, respectively. Based on the solution method of the intuitionistic fuzzy triple implication, the algorithm by using implication operator to 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 reasoning and fuzzy control. It also has scientific significance and application value.

薛占熬1，刘杰1，程慧茹2，王朋函1. 基于Lukasiewicz的直觉模糊三I 蕴涵算子 R I L[J]. 南京大学学报(自然科学版), 2015, 51(1): 99–104.

Xue Zhan’ao1, Liu Jie1, Cheng Huiru2, Wang Penghan1. Intuitionistic fuzzy triple I implication operator based on Lukasiewicz implication[J]. Journal of Nanjing University(Natural Sciences), 2015, 51(1): 99–104.

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