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首页> 外文期刊>Applied Soft Computing >Divergence-based cross entropy and uncertainty measures of Atanassov's intuitionistic fuzzy sets with their application in decision making
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Divergence-based cross entropy and uncertainty measures of Atanassov's intuitionistic fuzzy sets with their application in decision making

机译：atanassov直觉模糊套装在决策中的应用基于分歧的跨熵和不确定性措施

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摘要

The uncertainty measure of Atanassov's intuitionistic fuzzy sets (AIFSs) is important for information discrimination under intuitionistic fuzzy environment. Although many entropy measures and knowledge measures haven been proposed to depict uncertainty of AIFSs, how to measure the uncertainty of AIFSs is still an open topic. The relation between uncertainty and other measures like entropy measures, fuzziness and intuitionism is not clear. This paper introduces uncertainty measures by using new defined divergence-based cross entropy measure of AIFSs. Axiomatic properties of the developed uncertainty measure are analysis, together with the monotony property of uncertainty degree with respect to fuzziness and intuitionism. To adjust the contribution of fuzzy entropy and intuitionistic entropy on the total uncertainty, the proposed cross entropy and uncertainty measures are parameterized. Numerical examples indicate the effectiveness and agility of the biparametric uncertainty measure in quantifying uncertainty degree. Then we apply the cross entropy and uncertainty measures into an optimal model to determine attribute weights in multi-attribute group decision making (MAGDM) problems. A new method for intuitionistic fuzzy MAGDM problems is proposed to show the efficiency of proposed measures in applications. It is demonstrated by application examples that the proposed measures can get reasonable results coinciding with other existing methods. (C) 2019 Elsevier B.V. All rights reserved.
机译：Atanassov直觉模糊集（AIFS）的不确定性措施对于直觉模糊环境下的信息歧视非常重要。虽然许多熵措施和知识措施避难所被提出描绘AIFS的不确定性，但如何衡量AIFS的不确定性仍然是一个开放的主题。不确定度和其他措施之间的关系，如熵措施，模糊和直觉主义并不清楚。本文通过使用AIFS的新定义的分歧跨熵测量介绍了不确定性措施。发达的不确定性措施的公理性质是分析，以及关于模糊和直觉的不确定度的单调性质。为了调整模糊熵和直觉熵对总不确定性的贡献，参数化了建议的跨熵和不确定性措施。数值示例表示双轴不确定性测量在量化不确定性程度方面的有效性和灵活性。然后我们将跨熵和不确定性措施应用于最佳模型，以确定多属性组决策（MAGDM）问题中的属性权重。提出了一种新的直觉模糊MAGDM问题，以展示申请中提出措施的效率。应用程序示例证明了所提出的措施可以获得与其他现有方法重合的合理结果。 （c）2019年Elsevier B.V.保留所有权利。

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