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Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation

机译：基于相对偏好关系对三角形和梯形模糊数进行排序

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摘要

In this paper, we first propose a fuzzy preference relation with membership function representing preference degree to compare two fuzzy numbers. Then a relative preference relation is constructed on the fuzzy preference relation to rank a set of fuzzy numbers. Since the fuzzy preference relation is a total ordering relation satisfying reciprocal and transitive laws on fuzzy numbers, the relative preference relation satisfies a total ordering relation on fuzzy numbers as well. Normally, utilizing preference relation is more reasonable than defuzzification on ranking fuzzy numbers, because defuzzification does not present preference degree between two fuzzy numbers and loses some messages. However, fuzzy pair-wise comparison by preference relation is complex and difficult. To avoid above shortcomings, the relative preference relation adopts the strengths of defuzzification and fuzzy preference relation. That is to say, the relative preference relation expresses preference degrees of several fuzzy numbers over average as similar as the fuzzy preference relation does, and ranks fuzzy numbers by relative crisp values as defuzzification does. Thus utilizing the relative preference relation ranks fuzzy numbers easily and quickly, and is able to reserve fuzzy information.
机译：在本文中，我们首先提出一种模糊隶属关系，该隶属函数代表偏好程度，以比较两个模糊数。然后在模糊偏好关系上建立相对偏好关系，对一组模糊数进行排序。由于模糊偏好关系是满足关于模糊数的互逆和传递定律的总排序关系，因此相对偏好关系也满足关于模糊数的总排序关系。通常，利用优先级关系比对模糊数进行去模糊化更为合理，因为去模糊化不会在两个模糊数之间呈现优先级，并且会丢失一些消息。然而，通过偏好关系的模糊成对比较是复杂且困难的。为了避免上述缺点，相对偏好关系采用了去模糊化和模糊偏好关系的优势。就是说，相对偏好关系类似于模糊偏好关系，表示相对于平均值的几个模糊数的偏好度，并且像去模糊化那样，通过相对清晰的值对模糊数进行排名。因此，利用相对偏好关系可以容易且快速地对模糊数进行排序，并且能够保留模糊信息。

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