模糊推理三Ⅰ算法的还原性  

Reversibility of Triple Ⅰ Method for Fuzzy Reasoning

作　　者：李骏[1] 邓富喜[2] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050 [2]喀什师范学院数学系,新疆喀什844000

出　　处：《模糊系统与数学》2011年第5期7-12,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10771129);兰州理工大学优秀青年基金资助项目;兰州理工大学博士基金资助项目

摘　　要：模糊推理算法的还原性是判断蕴涵算子与推理方法配合效果的一个重要标准,只有蕴涵算子与推理方法搭配适当,才能使模糊推理有一个好的效果。本文对模糊推理三I算法具备还原性的条件进行了研究。首先,当与蕴涵算子相伴随的三角模为连续三角模时,给出了FM P问题三I算法具有还原性的充要条件;其次,当蕴涵算子为连续的正则蕴涵算子时,给出了FM T问题的三I算法具有还原性的充要条件;最后,当正则蕴涵算子关于补运算满足对合律时,给出了FM T问题三I算法满足还原性的一个充分条件。The reversibility of fuzzy inference methods is an important criterion to judge the effect of implication operators matching inference methods.Only the implication operators perfectly match inference methods can fuzzy reasoning have good effect.The present paper studies the condition that the triple I method of fuzzy reasoning satisfies the reversibility.A necessary and sufficient condition of reversibility of triple I method of Fuzzy Modus Ponens（FMP for short） is obtained when the t-norm adjoint to the given implication operator is continuous.A necessary and sufficient condition of reversibility of triple I method of Fuzzy Modus Tollens（FMT for short） is proved when the implication operator in FMT is continuous and regular.A sufficient condition of reversibility of triple I method of FMT is get in the case that the regular implication operators satisfy the involution law with respect to the complementary operator.

关 键 词：三I算法 还原性 正则蕴涵算子 FMP(Fuzzy MODUS Ponens) FMT(Fuzzy MODUS Tollens) 

分 类 号：O141[理学—数学]