Vague集转化为模糊集的动态犹豫度方法

A Dynamic Hesitancy Degree Method for Transforming Vague Set to Fuzzy Set

在Vague集转化为模糊集的过程中,将其犹豫度细分为赞成、反对和犹豫三部分,是一种动态的并且十分合理的方法。结合投票模型,通过还原和分析相关文献中犹豫度的细化过程发现,其每步细化中得到的赞成、反对,总是通过将上一步细化得到的最终的赞成、反对比例乘以最初的犹豫度π_A(x)而得到的,并在此基础上进而确定剩下的犹豫度,从而实现犹豫度的细分,而不管上一步细化后犹豫度是什么。考虑到每步细化后犹豫度一直在变化的事实,为此,提出一种将犹豫度细化的Vague集转化模糊集的一种动态方法,即通过在每步细化中将上一步细化获得最终的赞成、反对比例乘以上一步细化后得到的犹豫度,而得到本步细化后的赞成、反对,继而确定剩下的犹豫度,随后证明了该转化方法的合理性。最后,通过算例说了所提方法的可行性与有效性。

Subdividing the hesitancy degree of Vague set into three parts,agreement,disagreement and hesitation,is a dynamic and reasonable method in the process of transforming Vague set to fuzzy set.By taking voting model as an example and analyzing the process of subdivision on hesitancy degree in the reference,it is found that in every step of the subdivision on hesitancy degree,the new proportions of the agreement and disagreement are obtained by multiplying the initial hesitant degreeπ_A(x)with the final proportions of the agreement and disagreement in the last step,and thus the new proportions of the hesitancy degree is also formulated,which enabled the subdivision of the hesitancy degree of Vague sets,no matter what the hesitancy degree in the last step is.In fact,the hesitancy degree of Vague set is always changing in the process of subdivision.Based on dynamic hesitancy degree in the process of subdivision,a new dynamic hesitancy degree method for transforming Vague set to fuzzy set was proposed,which the new proportions of the agreement and disagreement are obtained by multiplying the hesitant degree in the last step with the final proportions of the agreement and disagreement in the last step,and thus the new proportions of the hesitancy degree is also formulated.And the rationality of the transformation was proved.Finally,some examples are given to show that the proposed method is effective and reasonable.