一类基于坐标变换的带参数直觉模糊距离构造方法

发布时间：2018-06-01 16:26

本文选题：直觉模糊集 + 软代数　；参考：《南京大学学报(自然科学)》2017年03期

【摘要】：1986年Atanassov提出直觉模糊集后,提出了多种直觉模糊集的距离公式,然而鲜有分析各种距离公式之间的差异.基于此,提出一种基于直觉模糊集三维坐标下的空间变换模型(隶属度、非隶属度、犹豫度),并证明了在坐标变换下,变换前后向量空间具备相同的代数性质和代数结构.在此基础上,构建了一系列新的直觉模糊集空间模型及其上的距离.尤其重要的是,提出了两类带参数的距离公式,而且该两类距离公式的排序能力都随着参数的变化而变化,现有经典直觉模糊集距离公式都是新距离公式的特例.因此,将所有距离公式依据其排序能力分成两大类:强序距离和弱序距离.仿真实验结果表明,强序距离在聚类、分类和模式识别中的表现明显优于弱序距离,公开数据库的手写体图像识别实验也证明强序距离在模式识别中的优势.
[Abstract]:After Atanassov put forward intuitionistic fuzzy sets in 1986, many distance formulas of intuitionistic fuzzy sets were put forward, but the differences between them were seldom analyzed. Based on this, a spatial transformation model based on intuitionistic fuzzy sets (membership degree, non-membership degree, hesitation degree) is proposed. It is proved that the vector space before and after the transformation has the same algebraic properties and algebraic structure under coordinate transformation. On this basis, a series of new intuitionistic fuzzy set space models and their distances are constructed. Especially, two kinds of distance formulas with parameters are proposed, and the sorting ability of these two kinds of distance formulas varies with the change of parameters. The existing classical intuitionistic fuzzy set distance formulas are special cases of new distance formulas. Therefore, all distance formulas are divided into two categories according to their ranking ability: strongly ordered distance and weakly ordered distance. The simulation results show that strong order distance is superior to weak order distance in clustering, classification and pattern recognition. The experiment of handwritten image recognition in open database also proves the advantage of strong order distance in pattern recognition.
【作者单位】：广东外语外贸大学经济贸易学院;暨南大学大数据决策研究所;广东外语外贸大学金融学院;
【基金】：国家自然科学基金(71271061) 广东省自然科学基金(2014A030313575,2016A030313688) 广东省软科学项目(2015A070704051) 广东省哲学社科项目(GD12XGL14) 广州市哲学社科项目(14G41) 广东省教育厅科技创新项目(2013KJCX0072) 全国统计科研重点项目(2016LZ18) 广东外语外贸大学重点创新团队项目(TD1605,15T21)
【分类号】：O159;TP391.41

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