计算机工程

• 人工智能及识别技术 • 上一篇    下一篇

直觉模糊熵的几何构造方法及其应用

(1. 安徽大学数学科学学院,合肥 230601;2. 安徽大学计算智能与信号处理教育部重点实验室,合肥 230039)   

  1. (1. 安徽大学数学科学学院,合肥 230601;2. 安徽大学计算智能与信号处理教育部重点实验室,合肥 230039)
  • 收稿日期:2012-08-15 出版日期:2013-11-15 发布日期:2013-11-13
  • 作者简介:毛军军(1973-),女,副教授、博士,主研方向:智能计算;姚登宝,博士研究生;刘二宝、王翠翠,硕士研究生
  • 基金项目:
    安徽省高等学校省级自然科学研究基金资助重点项目(KJ2013A033);安徽大学研究生创新基金资助项目(yfc100017, yfc1 00018);安徽大学学术创新团队基金资助项目(KJTD001B)

Geometry Construction Method for Intuitionistic Fuzzy Entropy and Its Application

(1. School of Mathematical Sciences, Anhui University, Hefei 230601, China; 2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China)   

  1. (1. School of Mathematical Sciences, Anhui University, Hefei 230601, China; 2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China)
  • Received:2012-08-15 Online:2013-11-15 Published:2013-11-13

摘要: 针对直觉模糊集中模糊性和直觉性对不确定信息的综合影响以及直觉模糊熵连续变化等问题,提出2种直觉模糊熵的几何构造方法,完善传统直觉模糊熵的构造准则。利用几何方法,分别通过建立等熵平面和等熵圆弧,结合距离构造2种新的直觉模糊熵,并证明其相关性质。论述直觉模糊熵的一般构造方法,对算例与现存的一些熵公式进行比较分析。将直觉模糊熵应用到多属性决策中,验证该方法的正确性和合理性。

关键词: 直觉模糊熵, 几何, 准则, 等熵平面, 等熵圆弧, 多属性决策

Abstract: Focusing on combining effects of uncertain information with the fuzziness and intuitionism and the continuous change of intuitionistic fuzzy entropy, this paper presents two geometry construction methods for intuitionistic fuzzy entropy. The classical construction criterion of intuitionistic fuzzy entropy is refined. By use of geometry methods, two new intuitionistic fuzzy entropies are presented through establishing isentropic plane and isentropic circle and distance, respectively, and relative properties are also proved. At the same time, the general construction method of intuitionistic fuzzy entropy is discussed, and compared with other existed entropy formulas by example. The reasonability and correction of the proposed methods are verified by applying the intuitionistic fuzzy entropy in multi-attributes decision-making problem.

Key words: intuitionistic fuzzy entropy, geometry, criterion, isentropic plane, isentropic circle, multi-attribute decision-making

中图分类号: