The Extended Alpha-triple I Algorithm Based on the Generalized Implication Operator

In this paper, the classical implication operator is generalized, and then the definition of generalized implication operator on [0, 1] is proposed. Based on generalized implication operator, the extended alpha-triple I principle is presented by generalizing the alpha-triple I algorithm. By analyzing the essence of alpha-triple Fuzzy Modus Ponens (FMP) and alpha-triple Fuzzy Modus Tollens (FMT) principles, and based on the generalized implication operator, the generalized calculating formula of extended alpha-triple I algorithm is proposed. At the same time, the reversibility on the proposed alpha-triple I algorithm is discussed. It is proved that Compositional Rule of Inference (CRI) is a special case of extended alpha-triple I algorithm. Finally, two implication operations are proposed to validate the proposed generalized equation.