The invariance property of fuzzy implication functions with respect to powers of t-norms is an interesting property in approximate reasoning. Although those fuzzy implication functions satisfying it have been recently fully characterized, the fulfillment of other important additional properties has not been investigated yet. As a first step in this line of research, in this paper the so-called strict T-power invariant implications, those implications which are invariant with respect to powers of a strict t-norm, are analyzed. From this study, it is proved that there are members of this family satisfying important properties such as the exchange principle, the law of importation or the iterative Boolean law, among others. This analysis leads to the characterization of the intersection of this family with the most usual classes of fuzzy implication functions.

模糊蕴涵函数相对于 t 范数的不变性是近似推理中的一个有趣特性。尽管满足它的那些模糊蕴涵函数最近已被充分表征，但尚未研究其他重要附加属性的实现。作为这方面研究的第一步，本文中所谓的严格T- 幂不变含义，即对严格 t 范数的幂不变的那些含义进行分析。从这项研究中可以证明，这个家族中存在满足交换原理、输入定律或迭代布尔定律等重要性质的成员。这种分析导致了该族与最常见的模糊蕴涵函数类别的交集的表征。