Various fuzzy sets have been developed in the recent years to model the uncertainty in judgments. Spherical fuzzy set (SFS) concept is one of these developments. It can provide an extensive preference domain for decision-makers by allowing them to state their hesitancy more explicitly. The peculiarity of SFS is that the squared sum of membership, nonmembership, and hesitancy degrees should be between 0 and 1 while each is independently defined in [0, 1]. In this study, ARAS as one of the most applied multiple attribute decision-making approaches is extended into a spherical fuzzy environment. Entropy-based and OWA operator-based objective attribute weights are also integrated with the newly proposed spherical fuzzy ARAS for coping with the drawbacks of subjective weighting such as longer data collection time and manipulation risk. The applicability of the proposition is shown in a hypothetical example of a product design problem and its robustness is shown by a comparative analysis.

中文翻译：

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球面模糊环境下集成客观属性加权的ARAS扩展

近年来，人们开发了各种模糊集来模拟判断的不确定性。球面模糊集 (SFS) 概念就是这些发展之一。它可以为决策者提供一个广泛的偏好域，允许他们更明确地表达他们的犹豫。SFS 的特点是成员资格、非成员资格和犹豫度的平方和应在 0 和 1 之间，而每个都在 [0, 1] 中独立定义。在这项研究中，ARAS 作为应用最广泛的多属性决策方法之一，被扩展到球形模糊环境中。基于熵和基于 OWA 算子的客观属性权重也与新提出的球形模糊 ARAS 相结合，以应对主观权重的缺点，例如较长的数据收集时间和操纵风险。