计算机科学 ›› 2019, Vol. 46 ›› Issue (10): 229-235.doi: 10.11896/jsjkx.180901738
张毛银, 郑婷婷, 郑婉容
ZHANG Mao-yin, ZHENG Ting-ting, ZHENG Wan-rong
摘要: 熵是刻画模糊集不确定性程度的一个重要手段。为刻画区间直觉模糊集的不确定性,首先基于区间数的Hukuhara差(简称H-差)提出区间直觉模糊集的核区间的概念,其能够有效反映区间直觉模糊集中隶属度与非隶属度的力量对比所产生的模糊性。考虑到区间直觉模糊集的不确定性由模糊性和犹豫性共同决定,提出了更符合人们直觉的区间直觉模糊集不确定度量的基本准则,由于区间直觉模糊集的模糊程度和犹豫程度所占比重并不能完全确定,因此为更好地描述两者对区间直觉模糊集不确定性程度的影响,利用指数函数加权的方法构造出一种新的区间直觉模糊熵。通过性质讨论和不同方法下区间直觉模糊熵的对比实例分析可知,在犹豫度区间长度相同的情况下,区间直觉模糊熵随着核区间的左右区间数的增大而减小;在核区间相同的情况下,区间直觉模糊熵随着犹豫度区间的左右区间数的增大而增大,符合其不确定性度量的基本准则。所提方法能充分反映不确定性随模糊性和犹豫性的增加而增加,这符合人们的直觉。其次,分析并验证了当区间直觉模糊集退化为直觉模糊集时,该方法构造的直觉模糊熵也能够有效度量直觉模糊集的不确定性程度。最后,将新的熵公式有效地应用到属性权重完全未知的多属性决策分析中,并通过实例验证了其合理性,为解决多属性决策问题提供了一种新的思路。
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