In the literature on Atanassov intuitionistic fuzzy sets, several methods have been proposed in order to obtain a ranking on intuitionistic fuzzy values. However, some problems may arise when working with these methods, such as the inadmissibility problem, the nonrobustness problem, the indifference problem, etc. Based on the concept of the Euclidean distance, we propose a novel approach for ranking intuitionistic fuzzy values, which addresses these problems. With the aid of its geometrical representation, we rank the intuitionistic fuzzy values in accordance with the following basic principle: The closer the intuitionistic fuzzy value is to the most favorable intuitionistic fuzzy value, the higher the ranking of the intuitionistic fuzzy value is. Moreover, we extend this approach by taking into account human cognitive bias, which reflects a decision maker's attitude toward positive or negative consequences in decision problems involving uncertainty. Finally, we generalize our approach by introducing the Minkowski distance, and show that the generalized approach also addresses the problems encountered by the existing methods.

中文翻译：

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直觉模糊值排序的欧几里得方法


在关于阿塔纳索夫直觉模糊集的文献中，已经提出了几种方法以获得直觉模糊值的排序。然而，使用这些方法时可能会出现一些问题，例如不可接受问题、非鲁棒性问题、冷漠问题等。基于欧几里得距离的概念，我们提出了一种对直觉模糊值进行排序的新方法，该方法解决了这些问题。借助其几何表示，我们按照以下基本原则对直觉模糊值进行排序：直觉模糊值越接近最有利的直觉模糊值，直觉模糊值的排名越高。此外，我们通过考虑人类认知偏见来扩展这种方法，这反映了决策者对涉及不确定性的决策问题的积极或消极后果的态度。最后，我们通过引入 Minkowski 距离来推广我们的方法，并表明该推广方法也解决了现有方法遇到的问题。