Pythagorean fuzzy sets (PFS) are an extension of intuitionistic fuzzy sets introduced by Atanassov [1]. PFSs have the advantage of providing larger domains for assigning membership and non-membership degrees satisfying that their squared sum is at most equal to one. PFS have been often used in modeling the problems under vagueness and impreciseness in order to better define the problems together with the hesitancy of decision makers. Different human emotions and behaviors can be modeled in humanoid robots (HR) by fuzzy sets. In this paper, facial expressions of a humanoid robot are modeled depending on the degrees of the emotions. Larger degree of emotion causes a stronger indicator of the facial mimic.

中文翻译：

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使用勾股模糊集对人形机器人面部表情建模

勾股模糊集（PFS）是Atanassov [1]引入的直觉模糊集的扩展。PFS的优点是提供更大的域来分配成员资格和非成员资格度，以满足其平方和最多等于1的要求。PFS通常用于模糊性和不精确性的问题建模，以便更好地定义问题以及决策者的犹豫。可以在人形机器人（HR）中通过模糊集对不同的人类情感和行为进行建模。在本文中，根据情感的程度对人形机器人的面部表情建模。较大程度的情绪会导致面部表情更强烈。