Differently implicational universal triple I method of (1, 2, 2) typeI

As a generalization of the triple I method, differently implicational universal triple I method of (1, 2, 2) type (universal triple I method for short) is investigated. First, the concepts of residual operators and strongly residual operators are given, and then related conclusions of residual pairs are provided. Second, the related universal triple I solutions (including FMP-solutions, FMT-solutions and so on) are strictly defined by the infimum, where such solutions are divided into two parts respectively corresponding to the minimum and infimum. Then, we put emphasis on the FMP-solutions, in which the unified forms of FMP-solutions w.r.t. strongly residual operators and a new idea for getting FMP-solutions w.r.t. infimum are achieved. Third, as a result of analyzing the logic basis of a sort of CRI (Compositional Rule of Inference) method, it is found that their CRI solutions can be regarded as special cases of FMP-solutions. Lastly, the response functions of fuzzy systems via universal triple I method are discussed, which demonstrates that the universal triple I method can provide bigger choosing space and get better fuzzy controllers by contrast with the triple I method and CRI method.