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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (1): 45-62.doi: 10.6040/j.issn.1671-9352.4.2023.0250

• • 上一篇    

图片模糊集的减法和除法算子研究

孟伟伟,郑婷婷*,刘钧歌,吴孝宇   

  1. 安徽大学数学科学学院, 安徽 合肥 230601
  • 发布日期:2025-01-10
  • 通讯作者: 郑婷婷(1978— ), 女,教授, 博士,研究方向为粒计算和知识发现. E-mail: tt-zheng@163.com
  • 作者简介:孟伟伟(1998— ), 女,硕士研究生, 研究方向为粒计算和知识发现. E-mail: mengww@stu.ahu.edu.cn*通信作者:郑婷婷(1978— ), 女,教授, 博士,研究方向为粒计算和知识发现. E-mail: tt-zheng@163.com
  • 基金资助:
    国家自然科学基金资助项目(61806001)

Study on subtraction and division operations over picture fuzzy sets

MENG Weiwei, ZHENG Tingting*, LIU Junge, WU Xiaoyu   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
  • Published:2025-01-10

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摘要： 针对图片模糊环境下完备的减法和除法问题, 构造加法和乘法的方程, 定义了图片模糊数(picture fuzzy numbers, PFNs)的减法和除法运算。基于距离最近导出各种情形下方程的最优解, 得出更加完备的PFNs的减法和除法运算法则。分析了2种PFNs算子及与加法、乘法混合运算的相关性质。将改进的2种算子以逐点的方式拓展到图片模糊集上,讨论了基本性质。通过算例分析验证该算子的适用性和可行性。

关键词: 图片模糊集, 线性规划, 减法算子, 除法算子, 模式识别

Abstract: Aiming at the problem of the complete subtraction and division problems under picture fuzzy environments, the subtraction and division operations of PFNs(picture fuzzy numbers, PFNs)are defined by constructing equations for addition and multiplication. Based on the nearest distances, the optimal solution of the equation is derived in various situations, and more complete subtraction and division operation algorithms are obtained. The properties of the two newly defined operators and the mixed operation of addition and multiplication are analyzed in detail. The two improved operators are extended in a pointwise manner to the picture fuzzy set, and the essential properties are discussed. The applicability and feasibility of this operator is verified through numerical analysis.

Key words: picture fuzzy set, linear programming, subtraction operation, division operation, pattern recognition

中图分类号: 

  • TP391
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