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Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

机译:直觉模糊数的运算和排序方法,综述和新方法

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Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have important interpretations in real application of IFNs. In this paper, we will first review the existing methods for ranking and arithmetic operations on several representations of IFNs. Then, we will propose a new method based on arithmetic mean and geometric mean to compute membership and non-membership degrees of resulted IFN from arithmetic operations on IFNs. It is caused that the resulted degrees don't change monotonousness and be closer to reality. Furthermore, a new method for ranking of IFNs will be proposed. Finally, the proposed methods are used in the numerical examples, compared to some other existing methods.
机译:直觉模糊数(IFN)传递的信息比不确定情况下的模糊数更多。导致许多其他人试图定义用于对IFN进行排名和对其进行算术运算的方法,这些方法被用于IFN的实际应用(例如决策)中。 IFN的算术运算符更改了成员资格和非成员资格程度。所获得的程度在实际应用IFN方面具有重要的解释。在本文中,我们将首先回顾对IFN几种表示形式进行排序和算术运算的现有方法。然后,我们将提出一种基于算术平均值和几何平均值的新方法,以计算对IFN进行算术运算得出的IFN的隶属度和非隶属度。导致所得到的度数不改变单调性而更接近于现实。此外,将提出一种新的IFN分级方法。最后,与其他一些现有方法相比,在数值示例中使用了所提出的方法。

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