Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

doi:10.23919/JSEE.2023.000015

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (2): 422-438.doi: 10.23919/JSEE.2023.000015

• • 上一篇

收稿日期:2021-10-04 出版日期:2023-04-18 发布日期:2023-04-18

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

Fuping LIAO(), Wu LI(), Gang LIU(), Xiaoqiang ZHOU()

¹ School of Information Science and Engineering, Hunan Institute of Science and Technology, Yueyang 414006, China

Received:2021-10-04 Online:2023-04-18 Published:2023-04-18
Contact: Wu LI E-mail:liaofuping1998@163.com;liwu0817@163.com;4350594@qq.com;zxq0923@163.com
About author:
LIAO Fuping was born in 1998. He received his B.E. degree from Hunan Institute of Science and Technology, Yueyang, China, in 2019, where he is pursuing his M.S. degree in information and communication engineering. His current research interests include decision analysis and clustering analysis. E-mail: liaofuping1998@163.com

LI Wu was born in 1977. He received his B.S. degree from Shenyang Ligong University, Shenyang, China, M.S. degree in power system and its automation from Xinan Jiaotong University, Chengdu, China, and Ph.D. degree in control science and engineering from Huazhong University of Science and Technology, Wuhan, China, in 2009. His current research interests include intelligent decision analysis and optimization. E-mail: liwu0817@163.com

LIU Gang was born in 1983. He received his B.Sc. and M.S. degrees from Naval Arms Command Institute, China, in 2005 and 2008, respectively, and Ph.D. degree from National University of Defense Technology (NUDT), China, in 2013. He is the deputy dean of the School of Information Science and Engineering, Hunan Institute of Science and Technology. His research interests include intelligent information processing, optimization, and path planning. E-mail: 4350594@qq.com

ZHOU Xiaoqiang was born in 1983. He received his B.S. degree from Jilin University, Jilin, China, M.S. degree in computer software and theory from Xiangtan University, Xiangtan, China, and Ph.D. degree in applied mathematics from Hunan University, Changsha, China, in 2014. His current research interests include decision analysis, information fusion, fuzzy mathematics, optimization algorithm, and machine learning. E-mail: zxq0923@163.com
Supported by:
The work was supported by the Key Research and Development Project of Hunan Province (2019SK2331), the Natural Science Foundation of Hunan Province (2019JJ40099;2019JJ40100;2020JJ4339), the Key Scientific Research Project of Hunan Education Department (18A317;19A202), the Scientific Research Fund of Hunan Provincial Education Department (20B272), and the Innovation Foundation for Postgraduate of Hunan Institute of Science and Technology (YCX2020A34)

摘要/Abstract

Abstract:

As a generalization of fuzzy set, hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information. As modern socioeconomic decision-making problems are becoming more and more complex, it also becomes more and more difficult to appropriately depict decision makers’ cognitive information in decision-making process. In order to describe the decision information more comprehensively, we define a pythagorean probabilistic hesitant triangular fuzzy set (PPHTFS) by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set. Firstly, the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element (PPHTFE) are proposed, and the comparison rule of two PPHTFEs is given. Then, some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed, and their properties are also studied. Finally, a multi-attribute decision-making (MADM) model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information, and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Key words: pythagorean probabilistic hesitant triangular fuzzy set (PPHTFS), aggregation operator, multi-attribute decision-making (MADM)

. [J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 422-438.

Fuping LIAO, Wu LI, Gang LIU, Xiaoqiang ZHOU. Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making[J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 422-438.

图/表 4

参考文献 41

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Tourism resource	${C}_{1}$	${C}_{2}$
$A_1$	$\langle\{[0.6,0.7,0.8\|0.4],[0.4,0.5,0.6\|0.6]\},\{[0.1,0.2,0.3\|1]\}\rangle$	$\langle\{[0.6,0.7,0.8\|1]\},\{[0.2,0.3,0.4\|1]\}\rangle$
$A_2$	$\langle\{[0,0.1,0.2\|1]\},\{[0.3,0.4,0.5\|1]\}\rangle$	$\langle\{[0.2,0.3,0.4\|1]\},\{[0.5,0.6,0.8\|1]\}\rangle$
$A_3$	$\langle\{[0.5,0.6,0.7\|1]\},\{[0.1,0.3,0.5\|1]\}\rangle$	$\langle\{[0.4,0.5,0.7\|1]\},\{[0.1,0.2,0.3\|1]\}\rangle$
$A_4$	$\langle\{[0,0.1,0.2\|0.8],[0.2,0.3,0.4\|0.2]\},\{[0.4,0.5,0.6\|1]\}\rangle$	$\langle\{[0.2,0.3,0.4\|1]\},\{[0.4,0.5,0.6\|0.8],[0.6,0.7,0.8\|0.2]\}\rangle$

Tourism resource	${C}_{3}$	${C}_{4}$
$A_1$	$\langle\{[0.1,0.2,0.3\|1]\},\{[0.1,0.2,0.3\|1]\}\rangle$	$\langle\{[0.4,0.5,0.6\|0.6],[0.6,0.7,0.8\|0.4]\},\{[0.2,0.3,0.4\|1]\}\rangle$
$A_2$	$\langle\{[0.1,0.2,0.3\|0.8],[0.3,0.4,0.5\|0.2]\},\{[0.6,0.7,0.8\|1]\}\rangle$	$\langle\{[0.2,0.3,0.4\|1]\},\{[0.2,0.3,0.4\|1]\}\rangle$
$A_3$	$\langle\{[0.6,0.7,0.8\|1]\},\{[0,0.1,0.2\|1]\}\rangle$	$\langle\{[0.1,0.2,0.3\|0.6],[0.3,0.4,0.5\|0.4]\},\{[0.3,0.4,0.5\|1]\}\rangle$
$A_4$	$\langle\{[0,0.1,0.3\|1]\},\{[0.7,0.8,0.9\|1]\}\rangle$	$\langle\{[0.1,0.2,0.3\|1]\},\{[0.5,0.6,0.7\|1]\}\rangle$

Tourism resource	$\text{PPHTFWA}$	$\text{PPHTFWG}$
$A_1$	$\left\{[0.49,0.59,0.69],[0.14,0.24,0.35]\right\}$	$\left\{[0.38,0.5,0.61],[0.16,0.26,0.35]\right\}$
$A_2$	$\left\{[0.16,0.25,0.34],[0.35,0.46,0.58]\right\}$	$\left\{[0,0.2,0.3],[0.42,0.52,0.66]\right\}$
$A_3$	$\left\{[0.45,0.55,0.68],[0,0.23,0.37]\right\}$	$\left\{[0.37,0.48,0.62],[0.17,0.28,0.42]\right\}$
$A_4$	$\left\{[0.12,0.21,0.31],[0.48,0.58,0.68]\right\}$	$\left\{[0,0.17,0.29],[0.51,0.62,0.73]\right\}$

Operator	Ordering
$\text{PPHTFWA}$	$A_1\succ A_3\succ A_2\succ A_4$
$\text{PPHTFWG}$	$A_1\succ A_3\succ A_2\succ A_4$

Method	Consideration of the non-membership degree of information	Description of information using probability features	Description of information by triangular fuzzy numbers	Description efficiency of people’s hesitation
Method in [35]	$\times$	$\times$	$\times$	$\checkmark$
Method in [24]	$\checkmark$	$\times$	$\times$	$\times$
Method in [25]	$\checkmark$	$\times$	$\checkmark$	$\times$
Method in [36]	$\times$	$\checkmark$	$\times$	$\checkmark$
The proposed method	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

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