This paper deals with a new transformation, so-called two-sided normalized (TSN), of continuous unimodal asymmetric probability distributions into possibility distributions. Many properties are derived and interpretations are discussed. A comparison with the optimal transformation is provided. In particular, the respective positions of right or left branches relative to the resulting optimal and TSN possibility distributions are given. It is also shown that the TSN transformation is the optimal transformation for the particular family of two-piece skewed distributions. The preservation of the asymmetry property is then analyzed and illustrated for several conventional asymmetric distributions and counter-examples of asymmetry preservation are provided. A multilinear approximation of the TSN transformation is finally proposed.

本文讨论了一种新的转换，即所谓的双边归一化 (TSN)，将连续单峰非对称概率分布转换为可能性分布。导出了许多属性并讨论了解释。提供了与最佳变换的比较。特别地，给出了右分支或左分支相对于所得最优分布和 TSN 可能性分布的各自位置。还表明 TSN 变换是两片偏态分布的特定族的最佳变换。然后分析和说明了几种常规不对称分布的不对称特性的保持，并提供了不对称保持的反例。最后提出了 TSN 变换的多线性近似。