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Applying preference relation method to determine the ranking order of fuzzy numbers

机译：应用偏好关系方法确定模糊数的排名顺序

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摘要

Ranking fuzzy numbers is an important issue for solving decision-making problems in a fuzzy environment. Many ranking approaches are developed in the literature for multi-criteria decision-making problems. Almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose. There is yet no method that can always give a satisfactory solution to every situation. Some ranking methods are counterintuitive, not discriminating or complex. Further, many of them produce different rankings for the same problems. This paper presents a new method for ranking fuzzy numbers based on the comparison of confidence intervals of these fuzzy numbers. For a given confidence value, a preference-relation function is defined to determine the degree of preference for each pair of fuzzy numbers. Since the preference relation is reciprocal and transitive, this method can rank more than two fuzzy numbers simultaneously and provide a total ordering for these fuzzy numbers. Furthermore, some important properties of this ranking method are verified and illustrated. Finally, two comparative examples are used to illustrate the feature in ranking fuzzy numbers.
机译：排名模糊数字是解决模糊环境中的决策问题的重要问题。许多排名方法是在文献中开发的，用于多标准决策问题。几乎所有现有的方法都专注于对排名目的的模糊数量的数量测量。然而，没有任何方法可以始终为每种情况提供令人满意的解决方案。一些排名方法是违反直觉的，而不是歧视或复杂。此外，许多人为同样问题产生不同的排名。本文提出了一种基于这些模糊数的置信区间的比较来排序模糊数的新方法。对于给定的置信度值，定义偏好关系功能以确定每对模糊数的偏好程度。由于偏好关系是倒数和传递的，因此该方法可以同时排列多于两个模糊数并为这些模糊数提供总排序。此外，验证和说明该排名方法的一些重要特性。最后，使用两个比较例用于说明排名模糊数中的特征。

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