剩余型直觉模糊推理的三Ⅰ方法

Triple Ⅰ method of intuitionistic fuzzy reasoning based on residual implicator

本文研究了由左连续三角模所生成的直觉三角模的性质,给出了与直觉三角模相伴随的剩余型直觉蕴涵算子的等价刻画,揭示了直觉模糊蕴涵算子和模糊蕴涵算子的关系.结合模糊推理的三Ⅰ方法,针对剩余型直觉蕴涵算子,提出直觉模糊推理IFMP问题的三Ⅰ方法和分解方法,给出两种方法的求解公式,并讨论了它们的还原性,证明了三Ⅰ方法和分解方法具有良好的还原性.最后提出了IFMP问题的α-三Ⅰ方法,并给出相应的算例分析.

This paper investigates the properties of the intuitionistic triangular norm induced by the leftcontinuous t-norm, and presents the equivalent characterization of intuitionistic residual implicator adjoint intuitionistic triangular norms, which clarifies the relationship between intuitionistic fuzzy implications and fuzzy implications. According to the triple I method of fuzzy reasoning, this paper proposes the triple I and decomposition methods for solving the IFMP problem of intuitionistic fuzzy reasoning for a residual intuitionistic implicator, and proposes two types of solving formulas. Moreover, this paper discusses the reductivity of the methods and shows that the triple I and decomposition methods for the IFMP problem possess the virtue of reductivity. Finally, the paper proposes the a-triple I method for the IFMP problem and provides a corresponding example.