【摘要】 本文提出了一种强FI代数-PFI代数,并且深入研究了它的性质,借此进一步揭示了FI-代数和剩余格之间更加密切的联系,进而以FI-代数为基本框架建立了R0-代数、正则剩余格等逻辑系统的结构特征(包括对隅结构)及其相互关系．这种以FI-代数为基础来统一处理剩余格和R0-代数的方法,同样适合于格蕴涵代数和MV代数等代数结构,而且从中更能清楚地看出它们之间的密切联系,也将有助于对相应形式逻辑系统与模糊推理的研究．更多还原

【Abstract】 In this paper, a new kind of the special fuzzy implication algebras-PFI-algebras are introduced, their fundamental properties are obtained, and the close connections between PFI-algebras and residuated lattices are established. Moreover, for (weak) R0-algebras and (strong) regular residuated lattices, their interrelation and the characterizations of interior structures (including dual structures) are established by the concept of the PFI-algebras. Those results will be useful for further studying the corresponding formal deductive systems and fuzzy reasoning.更多还原