直觉模糊二元合成补IFMT三I方法

针对构造直觉模糊蕴涵算子(IFIO)沿用Fuzzy集一元补导致出现的问题,对直觉模糊集(IFS)隶属函数和非隶属函数进行合成求补运算,提出了二元合成补的概念。给出了二元合成补的一些性质,证明了IFS的标准补和对合补是二元合成补的两个特例。构造了基于二元合成补的R0型IFIO,并应用于直觉模糊拒取式(IFMT)问题的三I方法。结果表明,基于二元合成补的IFIO构造方法简单,构造出的IFIO容易满足IFS定义的要求,具有的性质适合IFMT三I方法,并能保证该方法在一定条件下是还原算法。

Intuitionistic fuzzy dual compositional negator on triple I method for IFMT

To the problems of continuing to use unitary negators of Fuzzy sets in constructing Intuitionistic Fuzzy Implication Operators （IFIO）, a concept of dual compositional negator is proposed by using both membership function and non-membership function of Intuitionistic Fuzzy Sets （IFS） to compute compositional negator. Some properties of dual compositional negator are given and it is showed that the standard and involutive negators of IFS are two special cases of dual compositional negator. Then a IFIO of R0 based on dual compositional negator is constructed and applied on triple I method for Intuitionistic Fuzzy Modus Tollens （IFMT） problem. The results show that the constructing method of IFIO based on dual compositional negator is simpler, and the constructed IFIO is easy to satisfy the conditions of the IFS definition. It is also proved that the properties possessed by the constructed IFIO are fit for triple I method of IFMT, and can ensure that triple I method for IFMT is a reductive algorithm under some conditions.