System portfolio selection based on GRA method under hesitant fuzzy environment

doi:10.23919/JSEE.2022.000013

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (1): 120-133.doi: 10.23919/JSEE.2022.000013

• SYSTEMS ENGINEERING • Previous Articles Next Articles

System portfolio selection based on GRA method under hesitant fuzzy environment

Zhuoqian LI(), Yajie DOU*(), Boyuan XIA(), Kewei YANG(), Mengjun LI()

¹ College of Systems Engineering, National University of Defense Technology, Changsha 410073, China

Received:2020-08-31 Online:2022-01-18 Published:2022-02-22
Contact: Yajie DOU E-mail:zhuoqianli_nudt@163.com;yajiedou_nudt@163.com;xiaboyuan11@nudt.edu.cn;kayyang27@nudt.edu.cn;mjli11260744@sina.com
About author:|LI Zhuoqian was born in 1997. She is a postgraduate student at National University of Defense Technology. Her research interests are weapon alternative decision and effectiveness evaluation, and portfolio decision analysis. E-mail: zhuoqianli_nudt@163.com||DOU Yajie was born in 1987. He received his M.E. and Ph.D. degrees in management science and engineering from National University of Defense Technology. He is currently an associate professor in National University of Defense Technology. His research interests are weapon alternative decision and effectiveness evaluation, system-of-systems architecting and engineering management, and portfolio decision analysis. E-mail: yajiedou_nudt@163.com||XIA Boyuan was born in 1994. He received his B.E. degree in management science and engineering from National University and Defense Technology, Changsha, China, in 2017. He is currently a Ph.D. candidate in the College of Systems Engineering, National University of Defense Technology. His research interests include system of systems engineering, complex systems, and systems evaluation and optimization. E-mail: xiaboyuan11@nudt.edu.cn||YANG Kewei was born in 1977. He received his B.E. degree in systems engineering and Ph.D. degree in management science and engineering from the National University of Defense Technology, Changsha, Hunan, China, in 1999 and 2004, respectively. He is currently a professor and the Director of the Department of Management Science and Engineering, College of Systems Engineering, National University of Defense Technology. He was a visiting scholar with the Department of Computer Science at the University of York in the United Kingdom. His current research interests include intelligent agent simulation, defense acquisition, and system-of-systems requirement modeling. E-mail: kayyang27@nudt.edu.cn||LI Mengjun was born in 1964. He received his B.E. degree in the School of Economics and Finance from Xi’an Jiaotong University, Xi’an, China, in 1992, and Ph.D. degree in management science and engineering from the National University of Defense Technology, Changsha, China, in 2005. He was a visiting scholar at the University of Birmingham in the United Kingdom, in 2013. He is currently a professor of the Department of Management Science and Engineering, College of Systems Engineering, National University of Defense Technology. His research interest is defense acquisition. E-mail: mjli11260744@sina.com
Supported by:
This work was supported by the National Natural Science Foundation of China (71901214; 71690233)

Abstract

Abstract:

The hesitant fuzzy set (HFS) is an important tool to deal with uncertain and vague information. In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data; it is usually described by qualitative information and expressed as multiple possible values. We propose a method of equipment system portfolio selection under hesitant fuzzy environment. The hesitant fuzzy element (HFE) is used to describe the index and attribute values of the equipment system. The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system. The hesitant fuzzy grey relational analysis (GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree. Based on the score and hesitation degree of the equipment system, two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.

Key words: system portfolio selection, hesitant fuzzy set (HFS), grey relational analysis (GRA), score-hesitation tradeoff portfolio model

Zhuoqian LI, Yajie DOU, Boyuan XIA, Kewei YANG, Mengjun LI. System portfolio selection based on GRA method under hesitant fuzzy environment[J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 120-133.

Figures/Tables 9

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System	Criteria
System	$ {c_1} $	$ {c_2} $	$ {c_3} $	$ {c_4} $
$ {S_1} $	{0.45}	{0.35, 0.55, 0.60}	{0.70, 0.75, 0.80}	{0.60, 0.70}
$ {S_2} $	{0.35, 0.65, 0.75}	{0.20, 0.35}	{0.55, 0.7}	{0.45, 0.50}
$ {S_3} $	{0.75, 0.45}	{0.34, 0.45}	{0.62, 0.75}	{0.30, 0.45, 0.60}
$ {S_4} $	{0.55, 0.70}	{0.30, 0.56}	{0.3, 0.70}	{0.40}
$ {S_5} $	{0.35, 0.67}	{0.50, 0.60}	{0.73}	{0.42, 0.50}
$ {S_6} $	{0.30, 0.46, 0.63}	{0.45}	{0.35, 0.90}	{0.35, 0.54}
$ {S_7} $	{0.40, 0.45}	{0.22, 0.38, 0.50}	{0.70, 0.80, 0.85}	{0.70, 0.75}
$ {S_8} $	{0.50, 0.70}	{0.30, 0.55}	{0.55, 0.67}	{0.55}

System	$r_i^ + $	$r_i^ - $	${v_i}$	${\varphi _i}$
$ {S_1} $	0.664 6	0.655 7	0.503 4	0.049 7
$ {S_2} $	0.620 2	0.606 0	0.505 8	0.086 2
$ {S_3} $	0.670 4	0.391	0.554 3	0.098 1
$ {S_4} $	0.713 3	0.535 5	0.571 2	0.101 3
$ {S_5} $	0.786 1	0.540 7	0.592 5	0.062 5
$ {S_6} $	0.642 1	0.553 8	0.536 9	0.126 2
$ {S_7} $	0.606 0	0.724 8	0.455 4	0.056 8
$ {S_8} $	0.663 7	0.589 1	0.529 8	0.071 3

$ \theta $	${w_1}$	${w_2}$	${w_3}$	${w_4}$	${w_5}$	${w_6}$	${w_7}$	${w_8}$
0	0.2	0.05	0.05	0.05	0.25	0.05	0.199 8	0.150 2
1/9	0.2	0.05	0.05	0.072 9	0.25	0.05	0.05	0.277 1
2/9	0.2	0.05	0.05	0.168	0.25	0.05	0.05	0.182
3/9	0.2	0.05	0.05	0.263 2	0.25	0.05	0.05	0.086 8
4/9	0.118 7	0.05	0.05	0.3	0.25	0.05	0.05	0.131 3
5/9	0.05	0.05	0.101 2	0.3	0.25	0.05	0.05	0.148 8
6/9	0.05	0.05	0.2	0.3	0.25	0.05	0.05	0.05
7/9	0.05	0.05	0.2	0.3	0.25	0.05	0.05	0.05
8/9	0.05	0.05	0.2	0.3	0.25	0.05	0.05	0.05
1	0.05	0.05	0.2	0.3	0.25	0.05	0.05	0.05

Method	System sorting
The method of this article	${v_5} \succ {v_4} \succ {v_3} \succ {v_6} \succ {v_8} \succ {v_2} \succ {v_1} \succ {v_7}$
The traditional GRA	${v_5} \succ {v_4} \succ {v_3} = {v_8} \succ {v_1} \succ {v_6} \succ {v_2} \succ {v_7}$
TOPSIS	${v_5} \succ {v_3} \succ {v_4} \succ {v_1} \succ {v_2} = {v_6} \succ {v_8} \succ {v_7}$
Average $\bar h\left( x \right)$	${v_7} \succ {v_1} \succ {v_5} \succ {v_8} \succ {v_3} \succ {v_6} \succ {v_4} \succ {v_8}$

HFEs distance measure	Distance
The Hamming distance	${d_H}\left( {{h_1},{h_2}} \right) = {d_H}\left( {{h_1},{h_3}} \right) = 0.15$
The Euclidean distance	${d_E}\left( {{h_1},{h_2}} \right) = {d_E}\left( {{h_1},{h_3}} \right) = 0.158\;1$
The new Hamming distance proposed in this article	${d_{{\rm{IH}}}}\left( {{h_1},{h_2}} \right) = 0.2 < {d_{{\rm{IH}}}}\left( {{h_1},{h_3}} \right) = 0.35$
The new Euclidean distance proposed in this article	${d_{{\rm{IE}}}}\left( {{h_1},{h_2}} \right) = 0.165\;8 < {d_{{\rm{IE}}}}\left( {{h_1},{h_3}} \right) = 0.255$

System portfolio selection based on GRA method under hesitant fuzzy environment

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