论文标题
偏度，平均值和模糊数字的分散的新定义（度量） - 通过新表示形式作为参数化曲线
New definitions (measures) of skewness, mean and dispersion of fuzzy numbers -- by way of a new representation as parameterized curves
论文作者
论文摘要
我们给出了偏度的几何动机度量，定义一个平均值三角数，并（按该顺序）（以该顺序）分散数字，而无需参考或寻求与概率理论中的同名但平行概念相比。这些度量通过模糊数字的新表示形式分别作为参数化曲线，分别是其相关的切线束。重要的是，偏度和色散作为$α$（会员资格的程度）的功能，并且可以在每个$α$级别以及总体上分别给出。例如，当以模糊数字制定数学模型时，可以按照刻意的精度运行优化程序，从而封装了涉及的成员资格功能的特征，同时仅通过与实际变量和参数中的相同程序相比，仅通过相同的程序来增加计算复杂性。举例来说，这项工作为最近非常流行的模糊均值变化 - 统一投资组合优化提供了贡献。
We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory. These measures come about by way of a new representation of fuzzy numbers as parameterized curves respectively their associated tangent bundle. Importantly skewness and dispersion are given as functions of $α$ (the degree of membership) and such may be given separately and pointwise at each $α$-level, as well as overall. This allows for e.g., when a mathematical model is formulated in fuzzy numbers, to run optimization programs level-wise thereby encapsuling with deliberate accuracy the involved membership functions' characteristics while increasing the computational complexity by only a multiplicative factor compared to the same program formulated in real variables and parameters. As an example the work offers a contribution to the recently very popular fuzzy mean-variance-skewness portfolio optimization.
