一类带参数直觉模糊知识度量方法  

A knowledge measure with parameters of intuitionistic fuzzy sets

作　　者：张振华 林小龙 甘穗福 袁申国 胡勇 

机构地区：[1]广东外语外贸大学经济贸易学院,广州510006 [2]广东外语外贸大学信息学院,广州510006 [3]广东外语外贸大学金融学院,广州510006 [4]暨南大学大数据决策研究所,广州510632

出　　处：《南京大学学报（自然科学版）》2017年第6期1100-1113,共14页Journal of Nanjing University（Natural Science）

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)

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.Entropy and knowledge measure are important tools to express the uncertainty and certainty of fuzzy system,in which many achievements have been obtained.With the hesitancy degree,intuitionistic fuzzy sets（IFS）is more complex than traditional fuzzy sets in the ambiguity and uncertainty.Therefore,there are many deficiencies and shortcomings in the research of intuitionistic fuzzy entropy and intuitionistic fuzzy knowledge measurement,especially the lack of detailed research on the axiom system,unified theory and method.Hence,this paper first studies the axiom system presented by Szmidt and Kacprzyk,composed of non-negative boundedness,symmetry and order,and puts forward some necessary and sufficient conditions and necessary conditions for order property.Simultaneously,the order property of traditional classical operators is proved by using the necessary and sufficient conditions.Then a simple and convenient measurement model with parameter based on orderly condition is proposed,and it is proved that these models meet the axiom system.Finally,an experimental method to test the order property is proposed based on the intuitionistic fuzzy set.The experimental results show that the parametric model proposed in this paper are widely similar to the traditional algorithm under different parameter values,and the results of the presented method in some special values are more accurate than that of all classic models.The overall accuracy of our method is up to 98.73%,and the performance is excellent in all algorithms.

关 键 词：直觉模糊集 熵 正熵 负熵 知识度量 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]