基于区间数度量的区间值模糊集合的归一化距离、相似度、模糊度和包含度的关系研究

区间值模糊集合的距离、相似度、模糊度和包含度及其关系研究是区间值模糊集合的一个研究热点.考虑到区间值模糊集合所表示信息的丰富性,本文使用区间数而非实数来刻画区间值模糊集合的距离,首先给出基于区间数度量的区间值模糊集合的归一化距离的公理化定义,然后通过五个定理详细研究了基于公理化定义的区间值模糊集合的归一化距离、相似度、模糊度和包含度之间的相互转换关系,最后,给出了若干公式来计算基于区间数度量的区间值模糊集合的相似度、模糊度和包含度.这些结论,一方面丰富了区间值模糊集合的信息测度(距离、相似度、模糊度和包含度)的内容,另一方面也为区间值模糊集合的近似推理、决策分析、模式识别等领域的应用提供了新方法和新理论.

Relationship among the Normalized Distance, the Similarity Measure,the Entropy and the Inclusion Measure of Interval-valued Fuzzy Sets Based on Interval-number Measurement

The relationship research among the normalized distance,the similarity measure,the entropy and the inclusion measure of interval-valued fuzzy sets is a hot topic.Considering that the interval-valued fuzzy set includes more information than the ordinary fuzzy set.In this paper,we introduce an axiomatic definition of the normalized distance of the interval-valued fuzzy sets based on the interval-number measurement,investigate the relationship among the normalized distance,the similarity measure,the entropy and the inclusion measure of the interval-valued fuzzy sets in detail,prove five theorems that the normalized distance,the similarity measure,the entropy and the inclusion measure of the interval-valued fuzzy sets can be transformed by each other based on their axiomatic definitions and propose some formulas to calculate the similarity measure,the entropy and the inclusion measure of the interval-valued fuzzy sets.These conclusions can be applied in many fields such as approximate reasoning,decision-making analysis,pattern recognition and so on.