基于等量效果的Vague集转化为Fuzzy集的方法

Equivalent effect based method for transforming Vague sets into Fuzzy sets

当前Vague集转化为Fuzzy集的方法更多是根据直观,而没能详细阐述所基于的原理。为能更好理解Vague集转化为Fuzzy集的过程,考虑将Vague集转化为Fuzzy集模拟为一个最终无弃权票的多轮投票过程,从而构造了一种效果函数的定义,用以表示支持力度。并结合积分第一中值定理的意义提出了一种新的基于等量效果的转化方法,以保证在转化过程中,所关心的总效果没有发生变化。最后结合实例,严格分析了该方法的良好性质以及合理性。

Current methods about transforming Vague sets into Fuzzy sets are usually based on intuition, and they do not elaborate theory. In order to better understand the transforming process of Vague sets into Fuzzy sets, the process was simulated to be a multi-vote with no abstention at last, so as to put forward a kind of effect function definition to indicate the degree of support. To ensure that the overall effect of interest has not changed in the transformation process, a new method based on conversion of equivalent effect was proposed in view of the first mean value theorem for the integrals. Finally, the good nature and rationality of the method were rigorously analyzed according to the data.