您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (8): 77-87.doi: 10.6040/j.issn.1671-9352.0.2021.448

• • 上一篇    下一篇

广义区间值Pythagorean三角模糊集成算子及其决策应用

苏晓艳,陈京荣*,尹会玲   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 出版日期:2022-08-20 发布日期:2022-06-29
  • 作者简介:苏晓艳(1996— ),女,硕士研究生,研究方向为模糊决策理论与分析. E-mail:sxy199610@126.com*通信作者简介:陈京荣(1975— ),女,博士,教授,硕士生导师,研究方向为网络优化理论与设计. E-mail:chenjr@mail.lzjtu.cn
  • 基金资助:
    甘肃省自然科学基金资助项目(1610RJZA038)

Generalized interval-valued Pythagorean triangular fuzzy aggregation operator and application in decision making

SU Xiao-yan, CHEN Jing-rong*, YIN Hui-ling   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Online:2022-08-20 Published:2022-06-29

PDF (PC)

280

摘要： 针对连续集合上决策变量的隶属度和非隶属度之和超过1的决策问题,提出区间值Pythagorean三角模糊数,并且分析其广义集成算子的决策应用。首先,引入区间值Pythagorean三角模糊数的概念,得到其运算法则。其次,推导区间值Pythagorean三角模糊数的加权平均算子、加权几何算子、有序加权平均算子、有序加权几何算子、广义有序加权平均算子以及广义有序加权几何算子,介绍它们的相关性质。最后,构建出基于广义区间值Pythagorean三角模糊集成算子的多属性决策模型,并且根据实例对广义有序加权平均算子和广义有序加权几何算子进行稳定性分析,运用图像直观地证明在处理决策问题时前者优于后者,说明决策模型的有效性和可行性。

关键词: 区间值Pythagorean三角模糊数, 广义区间值Pythagorean三角模糊有序加权平均算子, 稳定性分析, 多属性决策

Abstract: In this article, the interval-valued Pythagorean triangular fuzzy number is proposed for the decision making problems when the sum of membership degree and non-membership degree of decision variables exceeds 1 on continuous sets, and the decision application of its generalized aggregation operator is analyzed. Firstly, the concept of interval-valued Pythagorean triangular fuzzy numbers is given, and its algorithm is obtained. Secondly, the weighted average operator, weighted geometric operator, ordered weighted average operator, ordered weighted geometric operator, generalized ordered weighted average operator and generalized ordered weighted geometric operator of interval-valued Pythagorean triangular fuzzy numbers are defined, and their related properties are introduced. Finally, a multi-attribute decision making model based on generalized interval-valued Pythagorean triangular fuzzy aggregation operator is constructed, and the stability of generalized ordered weighted average operator and generalized ordered weighted geometric operator is analyzed according to an example. The figures are used to prove intuitively that the former is superior to the latter when dealing with decision making problems. The effectiveness and feasibility of the decision making model are illustrated.

Key words: interval-valued Pythagorean triangular fuzzy number, generalized interval-valued Pythagorean triangular fuzzy ordered weighted average operator, stability analysis, multi-attribute decision making

中图分类号: 

  • O159
[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] YAGER R R, ABBASOV A M. Pythagorean membership grades, complex numbers and decision making[J]. International Journal of Intelligent Systems, 2013, 28(5):436-452.
[4] 何霞, 刘卫锋, 杜迎雪. 毕达哥拉斯三角模糊数集成算子及其决策应用[J]. 模糊系统与数学, 2019, 33(2):128-138. HE Xia, LIU Weifeng, DU Yingxue. Pythagorean triangular fuzzy numbers aggregation operators and application to decision making[J]. Fuzzy Systems and Mathematics, 2019, 33(2):128-138.
[5] 任耀军, 袁修久, 黄林, 等. 毕达哥拉斯三角犹豫模糊Muirhead平均算子的目标威胁评估应用[J]. 电光与控制, 2021, 28(4):16-20, 63. REN Yaojun, YUAN Xiujiu, HUANG Lin, et al. Pythagorean hesitant triangular fuzzy Muirhead mean operator and its application in target threat assessment[J]. Electronics Optics & Control, 2021, 28(4):16-20, 63.
[6] PENG Xindong, YANG Yong. Some results for Pythagorean fuzzy sets[J]. International Journal of Intelligent Systems, 2015, 30(11):1133-1160.
[7] PENG Xindong, YUAN Huiyong, YANG Yong. Pythagorean fuzzy information measures and their applications[J]. International Journal of Intelligent Systems, 2017, 32(10):991-1029.
[8] PENG Xindong, YANG Yong. Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators[J]. International Journal of Intelligent Systems, 2016, 31(5):444-487.
[9] GARG H. A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in the decision-making process[J]. International Journal of Intelligent Systems, 2017, 32(12):1247-1260.
[10] 万本庭, 路如意, 赖志卿. 区间值毕达哥拉斯模糊幂加权平均算子及群决策方法[J]. 计算机应用研究, 2020, 37(增刊2):184-187, 183. WAN Benting, LU Ruyi, LAI Zhiqing. Interval valued Pythagorean fuzzy power-weighted average operator and group decision making method[J]. Application Research of Computers, 2020, 37(Suppl. 2):184-187, 183.
[11] SHAKEEL M, ABDULLAH S, SHAHZAD M, et al. Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision-making[J]. Computational and Applied Mathematics, 2019, 10(10):2867-2886.
[12] YIARAYONG P. On interval-valued fuzzy soft set theory applied to ternary semigroups[J]. Lobachevskii Journal of Mathematics, 2021, 42(1):222-230.
[13] YOU Peng, LIU Xiaohe, SUN Jianbo. A multi-attribute group decision making method considering both the correlation coefficient and hesitancy degrees under interval-valued intuitionistic fuzzy environment[J]. Applied Soft Computing, 2021, 104:107187.
[14] 丁雪枫, 钟俊会. 一种基于区间值Pythagorean三角模糊语言集的多准则决策方法[J]. 上海大学学报, 2021, 27(1):190-207. DING Xuefeng, ZHONG Junhui. Multi-criteria decision-making method based on an interval-valued Pythagorean triangular fuzzy linguistic set[J]. Journal of Shanghai University, 2021, 27(1):190-207.
[15] ZHANG Jing, JIANG Yizhang. A study on mental health assessments of college students based on triangular fuzzy function and entropy weight method[J]. Mathematical Problems in Engineering, 2021, 2021(1):1-8.
[16] SHAKEEL M, ABDULLAH S, SAJJAD ALI KHAN M, et al. Averaging aggregation operators with interval Pythagorean trapezoidal fuzzy numbers and their application to group decision-making[J]. Journal of Mathematics, 2018, 50(2):147-170.
[17] 刘卫锋, 常娟, 何霞. 广义毕达哥拉斯模糊集成算子及其决策应用[J]. 控制与决策, 2016, 31(12):2280-2286. LIU Weifeng, CHANG Juan, HE Xia. Generalized Pythagorean fuzzy aggregation operators and applications in decision making[J]. Control and Decision, 2016, 31(12):2280-2286.
[1] 朱彦兰,周伟,褚童,李文娜. 管理委托下的双寡头博弈的复杂动力学分析[J]. 《山东大学学报(理学版)》, 2021, 56(7): 32-45.
[2] 黄林,袁修久,索中英,庞梦洋,包壮壮,李智伟. 区间值q阶犹豫模糊Frank集成算子及其决策应用[J]. 《山东大学学报(理学版)》, 2021, 56(3): 54-66.
[3] 杜文胜,徐涛. 广义正交模糊混合平均算子及其在多属性决策中的应用[J]. 《山东大学学报(理学版)》, 2021, 56(1): 35-42.
[4] 沈文昊, 乔坎坤, 卢志明. 金融股指稳定性的样本熵分析[J]. 山东大学学报（理学版）, 2014, 49(07): 50-56.
[5] 王中兴,唐芝兰,牛利利. 基于相对优势度的区间直觉模糊多属性决策方法[J]. J4, 2012, 47(9): 92-97.
[6] 苏丽娟 王文洽. 双边空间分数阶对流-扩散方程的一种有限差分解法[J]. J4, 2009, 44(10): 26-29.
[7] 章 玲,周德群 . λ模糊测度及其Mbius变换和关联系数间关系的推导[J]. J4, 2007, 42(7): 33-37 .
[8] 张方伟,曲淑英,王志强,姚炳学,曾现洋 . 偏差最小化方法及其在多属性决策中的应用[J]. J4, 2007, 42(3): 32-35 .
[9] 胡明礼,刘思峰 . 不完全信息下概率决策的扩展粗糙集方法[J]. J4, 2006, 41(6): 93-98 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报（理学版）, 2013, 48(1): 1 -22 .
[2] 何海伦， 陈秀兰*. 变性剂和缓冲系统对适冷蛋白酶MCP-01和中温蛋白酶BP-01构象影响的圆二色光谱分析何海伦， 陈秀兰*[J]. 山东大学学报（理学版）, 2013, 48(1): 23 -29 .
[3] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[4] 孙小婷1,靳岚2*. DOSY在寡糖混合物分析中的应用[J]. J4, 2013, 48(1): 43 -45 .
[5] 罗斯特,卢丽倩,崔若飞,周伟伟,李增勇*. Monte-Carlo仿真酒精特征波长光子在皮肤中的传输规律及光纤探头设计[J]. J4, 2013, 48(1): 46 -50 .
[6] 杨伦，徐正刚，王慧*，陈其美，陈伟，胡艳霞，石元，祝洪磊，曾勇庆*. RNA干扰沉默PID1基因在C2C12细胞中表达的研究[J]. J4, 2013, 48(1): 36 -42 .
[7] 冒爱琴1, 2, 杨明君2, 3, 俞海云2, 张品1, 潘仁明1*. 五氟乙烷灭火剂高温热解机理研究[J]. J4, 2013, 48(1): 51 -55 .
[8] 杨莹,江龙*,索新丽. 容度空间上保费泛函的Choquet积分表示及相关性质[J]. J4, 2013, 48(1): 78 -82 .
[9] 李永明1, 丁立旺2. PA误差下半参数回归模型估计的r-阶矩相合[J]. J4, 2013, 48(1): 83 -88 .
[10] 董伟伟. 一种具有独立子系统的决策单元DEA排序新方法[J]. J4, 2013, 48(1): 89 -92 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发