直觉模糊熵约束条件的改进及新模糊熵构造

doi:10.11772/j.issn.1001-9081.2015.12.3461

计算机应用 ›› 2015, Vol. 35 ›› Issue (12): 3461-3464.DOI: 10.11772/j.issn.1001-9081.2015.12.3461

直觉模糊熵约束条件的改进及新模糊熵构造

赵飞^1,2, 王青山¹, 郝万亮^3,4

1. 信息工程大学地理空间信息学院, 郑州 450001;
2. 95900部队, 河南开封 475003;
3. 信息工程大学导航与空天目标工程学院, 郑州 450001;
4

收稿日期:2015-05-18 修回日期:2015-07-24 出版日期:2015-12-10 发布日期:2015-12-10
通讯作者: 赵飞(1978-),男,河南邓州人,博士研究生,主要研究方向:信息理论与技术、战场环境分析与辅助决策
作者简介:王青山(1961-),男,湖北武汉人,教授,博士生导师,主要研究方向:信息理论与技术、战场环境分析与辅助决策;郝万亮(1982-),男,河南林州人,工程师,博士,主要研究方向:惯性导航、组合导航。

Improvement of constraint conditions and new constructional method for intuitionistic fuzzy entropy

ZHAO Fei^1,2, WANG Qingshan¹, HAO Wanliang^3,4

1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou Henan 450001, China;
2. Unit 95900, Kaifeng Henan 475003, China;
3. College of Navigation and Aerospace Engineering, Information Engineering University, Zhengzhou Henan 450001, China;
4. Unit 71687, Xinxiang Henan 453000, China

Received:2015-05-18 Revised:2015-07-24 Online:2015-12-10 Published:2015-12-10

摘要/Abstract

摘要： 为解决直觉模糊熵的定义和度量不合理问题,提出了一种直觉模糊熵的公理化定义并构造了新的度量方法。首先分析了现有直觉模糊熵的公理化定义中存在的差异并指出其缺陷和不足;接着提出了一种改进的直觉模糊熵的公理化定义,并构造了新的直觉模糊熵的计算公式;最后,通过实例,将新公式与现有直觉模糊熵公式进行了比较对比。算例分析表明,所提出的熵公式能够反映直觉模糊集的不确定性和模糊性,并且对直觉模糊集不确定性的区分能力更强。

关键词: 直觉模糊集, 直觉模糊熵, 隶属度, 不确定性

Abstract: To resolve the irrationality in the definition and measurement of intuitionistic fuzzy entropy, a new axiomatic definition for intuitionistic fuzzy entropy was proposed, and a new measuring formula was structured. Firstly, the existing differences in research of axiomatic definition for intuitionistic fuzzy entropy were analyzed, its defects and insufficiency were also pointed out. Secondly, an improved axiomatic definition for intuitionistic fuzzy entropy and a calculation formula of intuitionistic fuzzy entropy were proposed. Finally, the new formula was compared with the existing formulas for intuitionistic fuzzy entropy by examples. The results of the example analysis show that, the proposed entropy formula can reflect better the uncertainty and fuzziness of intuitionistic fuzzy sets, and the capability to discriminate the uncertainty of intuitionistic fuzzy sets is stronger.

Key words: intuitionistic fuzzy set, intuitionistic fuzzy entropy, membership degree, uncertainty

中图分类号:

TP18

赵飞, 王青山, 郝万亮. 直觉模糊熵约束条件的改进及新模糊熵构造[J]. 计算机应用, 2015, 35(12): 3461-3464.

ZHAO Fei, WANG Qingshan, HAO Wanliang. Improvement of constraint conditions and new constructional method for intuitionistic fuzzy entropy[J]. Journal of Computer Applications, 2015, 35(12): 3461-3464.

参考文献

[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-356.
[2] ATANASSOV K. Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] ATANASSOV K, GARGOV G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3):343-349.
[4] GAU W L, BUEHRER D J. Vague sets[J]. IEEE Transactions on Systems, Man and Cybernetics, 1993, 23(2):610-614.
[5] ZADEH L A. The concept of a linguistic variable and its applications to approximate reasoning[J]. Information Science, 1975, 8(1):199-249.
[6] BUSTINCE H, BURILLO P. Vague sets are intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1996, 79(3):403-405.
[7] CORNELIS C, ATANASSOV K T, KERRE E E. Intuitionistic fuzzy sets and interval-valued fuzzy sets:a critical comparison[C]//EUSFLAT'03:Proceedings of the 3rd European Conference on Fuzzy Logic and Technology. Berlin:Springer, 2003:159-163.
[8] DESCHRIJVER G, KERRE E E. On the relationship between some extensions of fuzzy set theory[J]. Fuzzy Sets and Systems, 2003, 133(2):227-235.
[9] BURILLO P, BUSTINCE H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J]. Fuzzy Sets and Systems, 2001, 118(3):305-316.
[10] SZMIDT E, KACPRZYK J. Entropy for intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 2001, 118(3):467-477.
[11] ZHANG Q, JIANG S. A note on information entropy measures for vague sets and its application[J]. Information Sciences, 2008, 178(21):4184-4191.
[12] WEI C, GAO Z,GUO T. An intuitionistic fuzzy entropy measure based on trigonometric function[J]. Control and Decision, 2012, 27(4):571-574. (魏翠萍,高志海,郭婷婷.一个基于三角函数的直觉模糊熵公式[J].控制与决策,2012,27(4):571-574.)
[13] FAN P. Measurement analysis for fuzzy entropy of Vague sets[J]. Computer Engineering and Applications, 2012,48(1):57-59. (范平.关于Vague集模糊熵的度量分析[J].计算机工程与应用,2012,48(1):57-59.)
[14] WEI C, LIANG X, ZHANG Y. A comparative analysis and improvement of entropy measure for intuitionistic fuzzy sets[J]. Journal of Systems Science and Mathematical Sciences, 2012,32(11):1437-1448. (魏翠萍,梁霞,张玉忠.直觉模糊集的熵公式比较与改进[J].系统科学与数学,2012,32(11):1437-1448.)
[15] WANG J, WANG P. Intuitionistic linguistic fuzzy multi-criteria decision-making method based on intuitionistic fuzzy entropy[J]. Control and Decision, 2012, 27(11):1694-1698. (王坚强,王佩.基于直觉模糊熵的直觉语言多准则决策方法[J].控制与决,2012,27(11):1694-1698.)
[16] XU F. New fuzzy entropy of Vague sets[J]. Computer Engineering and Science, 2012, 34(1):108-110. (徐凤生.Vague集的新模糊熵[J].计算机工程与科学,2012,34(1):108-110.)
[17] GAO M, SUN T. Constraint conditions and new constructional method of Vague entropy[J]. Computer Engineering and Applications, 2012, 48(18):27-31. (高明美,孙涛.Vague熵的约束条件和新模糊熵的构造[J].计算机工程与应用,2012,48(18):27-31.)
[18] ZHU L, YANG B, CHEN J. The constructional research of fuzzy entropy of Vague sets[J]. Pattern Recognition and Artificial Intelligence, 2006, 19(4):481-484. (朱六兵,杨斌,陈纪东.Vague集模糊熵的构造方法研究[J].模式识别与人工智能,2006,19(4):481-484.)
[19] LI F, LU A, AN Y. Fuzzy entropy of Vague sets and its construction method[J]. Journal of Huazhong University of Science and Technology, 2001, 29(9):1-3. (李凡,卢安,安余智.一类Vague集模糊熵的构造方法[J].华中科技大学学报,2001,29(9):1-3.)
[20] PENG F, LIANG J, WU H. New construction method of fuzzy entropy of Vague sets[J]. Computer Engineering and Applications, 2009, 45(29):52-54. (彭芳艳,梁家荣,伍华健.Vague集模糊熵的新构造方法[J].计算机工程与应用,2009,45(29):52-54.)
[21] GAO M, SUN T, ZHU J.Revised axiomatic definition and structural formula of intuitionistic fuzzy entropy[J]. Control and Decision, 2014, 29(4):470-474. (高明美,孙涛,朱建军.一种改进的直觉模糊熵公理化定义和构造公式[J].控制与决策,2014,29(4):470-474.)
[22] VLACHOS I K, SERGIADIS G D. Inner product based entropy in the intuitionistic fuzzy setting[J]. International Journal of Uncertainty Fuzziness Knowledge-Based System, 2006, 14(3):351-366.

直觉模糊熵约束条件的改进及新模糊熵构造

Improvement of constraint conditions and new constructional method for intuitionistic fuzzy entropy

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

[1]	曹玉红, 徐海, 刘荪傲, 王紫霄, 李宏亮. 基于深度学习的医学影像分割研究综述[J]. 计算机应用, 2021, 41(8): 2273-2287.
[2]	张林发, 张榆锋, 王琨, 李支尧. 基于直觉模糊集和亮度增强的医学图像融合[J]. 计算机应用, 2021, 41(7): 2082-2091.
[3]	周美玲, 陈淮莉. 基于负荷平衡的电动汽车模糊多目标充电调度算法[J]. 计算机应用, 2021, 41(4): 1192-1198.
[4]	李凯, 李洁. 基于pinball损失的结构模糊多分类支持向量机算法[J]. 《计算机应用》唯一官方网站, 2021, 41(11): 3104-3112.
[5]	裴仪瑶, 郭会明, 张丹普, 陈文博. 基于定位不确定性的鲁棒3D目标检测方法[J]. 计算机应用, 2021, 41(10): 2979-2984.
[6]	郭曙杰, 李志华, 蔺凯青. 云环境下基于模糊隶属度的虚拟机放置算法[J]. 计算机应用, 2020, 40(5): 1374-1381.
[7]	杜航原, 裴希亚, 王文剑. 面向属性网络的重叠社区发现算法[J]. 计算机应用, 2019, 39(11): 3151-3157.
[8]	杨晨, 王婕婷, 李飞江, 钱宇华. 基于概率的支持向量数据描述方法[J]. 计算机应用, 2019, 39(11): 3134-3139.
[9]	翟俊海, 张素芳, 王聪, 沈矗, 刘晓萌. 基于MapReduce的大数据主动学习[J]. 计算机应用, 2018, 38(10): 2759-2763.
[10]	周伟, 罗建军, 靳锴, 王凯. 基于模糊高斯学习策略的粒子群进化融合算法[J]. 计算机应用, 2017, 37(9): 2536-2540.
[11]	邓达平, 谢小云, 郭子璇. 直觉模糊环境下考虑有限理性特征的决策方法[J]. 计算机应用, 2017, 37(5): 1376-1381.
[12]	汤建国, 汪江桦. 基于粗糙集的古典密码模型[J]. 计算机应用, 2017, 37(4): 993-998.
[13]	徐伟, 李文根, 张毅超, 关佶红. 路网中位置不确定的二元反kNN查询[J]. 计算机应用, 2017, 37(2): 341-346.
[14]	霍纬纲, 屈峰, 程震. 基于演进向量量化聚类的增量模糊关联分类方法[J]. 计算机应用, 2017, 37(11): 3075-3079.
[15]	肖满生, 肖哲. 抑制式模糊C均值聚类惩罚因子的改进[J]. 计算机应用, 2016, 36(9): 2427-2431.