Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (8): 44-47.DOI: 10.3778/j.issn.1002-8331.1701-0009

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Property analysis of triple I method for Lukasiewicz intuitionistic fuzzy reasoning

LI Jun, LIU Yan   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China
  • Online:2018-04-15 Published:2018-05-02


李  骏,刘  岩   

  1. 兰州理工大学 理学院,兰州 730050

Abstract: The two basic reasoning models of intuitionistic fuzzy reasoning are Intuitionistic Fuzzy Modus Ponens(IFMP) and Intuitionistic Fuzzy Modus Tollens(IFMT) respectively. A kind of distance between intuitionistic fuzzy sets is introduced by the natural distance between classical fuzzy sets in the present paper. It is proven that both the triple I methods for solving IFMP and IFMT problems based on Lukasiewicz intuitionistic fuzzy implication are continuous with respect to this distance. Some sufficient conditions to guarantee the approximation property of the triple I methods for solving IFMP and IFMT are given respectively.

Key words: intuitionistic fuzzy set, intuitionistic fuzzy reasoning, triple I method, continuity, approximation property

摘要: 直觉模糊推理的两个基本模型是Intuitionistic Fuzzy Modus Ponens(IFMP)和Intuitionistic Fuzzy Modus Tollens(IFMT)。首先利用经典模糊集之间的自然距离定义了直觉模糊集间的一种距离。其次,证明了基于Lukasiewicz直觉模糊蕴涵的IFMP和IFMT问题的三I方法关于该距离都具有连续性,并且分别给出了IFMP和IFMT问题的三I方法满足逼近性的充分条件。

关键词: 直觉模糊集, 直觉模糊推理, 三I方法, 连续性, 逼近性