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模糊推理的FMT-泛五Ⅰ方法
FMT-universal Quintuple Implicational Method of Fuzzy Reasoning
【摘要】 在模糊推理领域中,采用五个蕴涵算子的五元蕴涵原理(QIP)方法是三Ⅰ方法的一种拓展.这里进一步将异蕴涵的思想引入其中,从而提出了面向FMT(fuzzy modus tollens)问题的泛五Ⅰ方法(简称为FMT-泛五Ⅰ方法).首先,建立了FMT-泛五Ⅰ方法的基本框架,包括解的定义和基本性质.其次,针对R-蕴涵算子证明了FMT-泛五Ⅰ方法的统一形式的解;并且针对一些具体的R-蕴涵算子提供了具体的解.然后,从FMT-泛五Ⅰ方法的内在机理出发,验证了其推理的还原性.最后,通过两个例子进行了模糊推理的计算和对比分析,并发现FMT-泛五Ⅰ方法比QIP方法的解更优.总而言之,作为面向FMT的QIP方法的推广,FMT-泛五Ⅰ方法提供了更多的选择空间,能获得更多更好的推理策略.
【Abstract】 In the field of fuzzy reasoning, the quintuple implication principle(QIP) method using five implication operators is an extension of the triple I method.We further introduce the differently implicational idea into it, and then propose the universal quintuple implicational method for the Fuzzy Modus Tollens(FMT) problem(FMT-universal quintuple implicational method for short).Firstly, the basic framework of FMT-universal quintuple implicational method is established, including the definition and basic properties of its solutions.Secondly, the unified form of solutions of FMT-universal quintuple implicational method is proved for R-implication operators.The solutions for some specific R-implication operators are also provided.Then, starting from the intrinsic mechanism of FMT-universal quintuple implicational method, the reasoning reducibility is verified.Finally, two examples are used to calculate and compare the fuzzy reasoning results, and it is found that the FMT-universal quintuple implicational method is better than the QIP method.In a word, as a generalization of the QIP method for FMT,the FMT-universal quintuple implicational method can provide more choice space, and obtain more and better inference strategies.
【Key words】 Fuzzy Reasoning; Implication Operator; Triple I Method; Universal Triple Ⅰ Method; Different Implications; Universal Quintuple Implicational Method;
- 【文献出处】 模糊系统与数学 ,Fuzzy Systems and Mathematics , 编辑部邮箱 ,2025年03期
- 【分类号】O159
- 【下载频次】5