一类带参数直觉模糊知识度量方法

发布时间：2018-11-18 18:33

【摘要】：熵和知识测度是表示模糊系统不确定性和有序性程度的重要工具,目前已有诸多研究成果.直觉模糊集比传统模糊集多了犹豫度向量,其模糊性和不确定性比传统模糊集更复杂.因此,在直觉模糊熵和直觉模糊知识度量领域,现有研究存在诸多不足,尤其缺乏对公理体系的细化研究,算子之间的对比和遴选缺乏统一的理论和方法指导.基于此,首先对Szmidt和Kacprzyk的公理体系开展研究,将基本性质分成非负有界、对称性和有序性,并针对有序性提出了一些易于判定的充分必要条件和必要条件.同时,利用可导条件下的有序性条件,对传统经典算子的有序性进行了证明.并依据有序性条件提出了新型的简便的带参数知识度量模型,同时证明这些模型满足公理体系.最后,从直觉模糊集合套构造,提出了检验是否满足有序性的实验方法,并对所提出的带参数模型在不同参数取值下与传统经典算法进行对比.实验结果表明,该带参数模型在不同参数取值下与传统算法的结果具有广泛的相似性,且特殊取值下的运算结果精度更高,总体精度高达98.73%,在所有算法中表现优秀.
[Abstract]:Entropy and knowledge measure are important tools to express the degree of uncertainty and order of fuzzy systems. The intuitionistic fuzzy set has more hesitancy vectors than the traditional fuzzy set, and its fuzziness and uncertainty are more complex than the traditional fuzzy set. Therefore, in the field of intuitionistic fuzzy entropy and intuitionistic fuzzy knowledge measurement, there are many deficiencies in the existing research, especially the lack of detailed research on axiom system, and the lack of unified theory and method guidance for the comparison and selection of operators. Based on this, the axioms of Szmidt and Kacprzyk are studied firstly, and the basic properties are divided into non-bearing bounds, symmetry and ordering, and some necessary and sufficient conditions for ordering are proposed. At the same time, the orderliness of the traditional classical operators is proved by using the order condition under the derivable condition. According to the order condition, a new and simple knowledge measurement model with parameters is proposed, and it is proved that these models satisfy the axiom system. Finally, from the construction of intuitionistic fuzzy sets, an experimental method is proposed to test whether orderliness is satisfied or not, and the proposed model with parameters is compared with the traditional classical algorithm under different parameters. The experimental results show that the model with parameters has a wide similarity with the results of the traditional algorithm under different parameter values, and the precision of the operation results with special values is higher, the overall accuracy is up to 98.733.The model performs well in all the algorithms.
【作者单位】：广东外语外贸大学经济贸易学院;广东外语外贸大学信息学院;广东外语外贸大学金融学院;暨南大学大数据决策研究所;
【基金】：国家自然科学基金(71271061) 国家统计局全国统计科研计划重点项目(2016LZ18) 广东省自然科学基金(2014A030313575,2016A030313688) 广东省软科学项目(2015A070704051) 广东省哲学社会科学项目(GD12XGL14) 广东省质量工程项目(125-XCQ16268) 广州市哲学社会科学项目(14G41,2017GZYB45) 广东省教育厅科技创新项目(2013KJCX0072) 广东外语外贸大学特色创新项目(15T21);广东外语外贸大学重点创新团队项目(TD1605);广东外语外贸大学高等教育重点项目(2016GDJYYJZD004,GYJYZDA14002) 大学生创新创业训练计划(201711846004)
【分类号】：O159

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