Mission capability assessment of UAV swarms based on UAF and interval-valued spherical fuzzy ANP

doi:10.23919/JSEE.2026.000017

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (1): 225-241.doi: 10.23919/JSEE.2026.000017

• SYSTEMS ENGINEERING • Previous Articles Next Articles

Mission capability assessment of UAV swarms based on UAF and interval-valued spherical fuzzy ANP

Minghao LI(), An ZHANG(), Wenhao BI(), Qiucen FAN(), Pan YANG()

School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received:2023-08-04 Online:2026-02-18 Published:2026-03-09
Contact: An ZHANG E-mail:liminghao@mail.nwpu.edu.cn;zhangan@nwpu.edu.cn;biwenhao@nwpu.edu.cn;fanqc1006@mail.nwpu.edu.cn;xyyangpan@mail.nwpu.edu.cn
About author:
LI Minghao was born in 1997. He received his B.S. degree from Northwestern Polytechnical University in 2018. He is currently working toward his Ph.D. degree in aeronautical and astronautical science and technology. His research interests include unmanned aerial vehicle swarm control and effectiveness assessment of system of systems. E-mail: liminghao@mail.nwpu.edu.cn

ZHANG An was born in 1962. He received his M.S. and Ph.D. degrees from Northwestern Polytechnical University in 1986 and 1999, respectively. He is currently a professor with Northwestern Polytechnical University. His research interests include system of systems engineering, unmanned aerial vehicle swarm control, and effectiveness assessment of system of systems. E-mail: zhangan@nwpu.edu.cn

BI Wenhao was born in 1986. He received his Ph.D. degree from Northwestern Polytechnical University, in 2018. He is currently an associate researcher with Northwestern Polytechnical University. His research interests include effectiveness assessment, system engineering and evidence theory. E-mail: biwenhao@nwpu.edu.cn

FAN Qiucen was born in 1996. He received his M.S. degree from Northwestern Polytechnical University in 2022. He is currently working toward his Ph.D. degree in aeronautical and astronautical science and technology. His research interests include model-based systems engineering and system of systems modeling.E-mail: fanqc1006@mail.nwpu.edu.cn

YANG Pan was born in 1996. She received her B.S. degree from Northwestern Polytechnical University in 2017. She is currently working toward her Ph.D. degree in aeronautical and astronautical science and technology. Her research interests include unmanned aerial vehicle swarm control and multi-agent systems. E-mail: xyyangpan@mail.nwpu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (62073267; 61903305), and the Fundamental Research Funds for the Central Universities (HXGJXM202214).

Abstract

Abstract:

For mission-oriented unmanned aerial vehicle (UAV) swarms, mission capability assessment provides an important reference in the design and development process, and is a precondition for mission success. For this multi-criteria decision-making (MCDM) problem, the current literature lacks a way to unambiguously present criteria and the popular fuzzy analytic network process (ANP) approaches neglect the hesitancy of subjective judgments. To fill these research gaps, an MCDM method based on unified architecture framework (UAF) and interval-valued spherical fuzzy ANP (IVSF-ANP) is proposed in this paper. Firstly, selected viewpoints in UAF are extended to construct criteria models with standardized representation. Secondly, interval-valued spherical fuzzy sets are introduced to ANP to weight interdependent criteria, handling fuzziness and hesitancy in pairwise comparisons. A method of adjusting weights of experts based on their decision similarities is also included in this process to reduce ambiguity brought by multiple experts. Next, performance characteristics are non-linearly transformed regarding to expectations to get final results. This proposition is applied to assess the mission capability of UAV swarms to search and strike surface vessels. Comparative analysis shows that the proposed method is valid and reasonable.

Key words: unmanned aerial vehicle (UAV) swarm, capability assessment, multi-criteria decision-making (MCDM), unified architecture framework, interval-valued spherical fuzzy set, analytical network process (ANP)

Minghao LI, An ZHANG, Wenhao BI, Qiucen FAN, Pan YANG. Mission capability assessment of UAV swarms based on UAF and interval-valued spherical fuzzy ANP[J]. Journal of Systems Engineering and Electronics, 2026, 37(1): 225-241.

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References 42

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Linguistic term	IVSFN	Consistency scale
Equally important (EI)	([0.45, 0.55], [0.45, 0.55], [0.30, 0.40])	1
Moderately more important (MMI)	([0.55, 0.65], [0.35, 0.45], [0.25, 0.30])	3
Strongly more important (SMI)	([0.65, 0.75], [0.25, 0.35], [0.20, 0.25])	5
Very strongly more important (VSMI)	([0.75, 0.85], [0.15, 0.25], [0.15, 0.20])	7
Absolutely more important (AMI)	([0.85, 0.95], [0.05, 0.15], [0.05, 0.15])	9
Moderately less important (MLI)	([0.35, 0.45], [0.55, 0.65], [0.25, 0.30])	1/3
Strongly less important (SLI)	([0.25, 0.35], [0.65, 0.75], [0.20, 0.25])	1/5
Very Strongly less important (VSLI)	([0.15, 0.25], [0.75, 0.85], [0.15, 0.20])	1/7
Absolutely less important (ALI)	([0.05, 0.15], [0.85, 0.95], [0.05, 0.15])	1/9

UAV parameter	UAV1	UAV2	UAV3	UAV4	UAV5
Search radius/m	3000	2000	2500	1800	1500
Direction locating error	1	0.8	1.3	1.5	0.7
Cruise speed/(m/s)	20	25	40	50	30
Wingspan/m	3.5	3.4	4.2	4	2
Wing area/m²	1.6	1.22	1.5	1.2	0.4
Lift coefficient	0.50	0.98	0.26	0.60	1.02
Drag coefficient	0.035	0.016	0.035	0.038	0.040
Lift curve slope	0.089	0.092	0.041	0.089	0.150
Operational time/min	180	120	240	520	60
Payload/kg	40	30	60	120	15
Jamming coefficient	1	1.2	0.9	0.8	0.7
Operational altitude/m	1000	1600	2000	3000	500
Data transmission rate/kbps	640	115	128	276	212
Link security	0.85	0.93	0.81	0.78	0.8
Link power consumption/W	13.5	6.7	5	3.2	7.8

Performance characteristic	S1	S2	S3	S4	S5
Total covered search area/km²	29.69	13.51	20.81	11.03	7.78
Target locating average error	909.1	1384.53	1127.03	1533.4	1841.07
Cruise speed/(m/s)	20	25	40	50	30
Lift to drag change	0.25	0.16	0.12	0.08	0.14
Operational time/min	180	120	240	520	60
Formation width/m	182.68	213.45	178.06	243.62	169.66
Payload of single UAV/kg	40	30	60	120	15
Jamming to signal ratio	0.74	0.89	0.66	0.59	0.52
Operational altitude/m	1000	1600	2000	3000	500
Formation generating time/s	99.62	87.24	278.55	153.56	213.23
Data transmission rate/kbps	640	115	128	276	212
Link security	0.85	0.93	0.81	0.78	0.8
Link power consumption/W	13.5	6.7	5	3.2	7.8

Expert	Sub-capability	C51	C52	C53	CR
Expert 1	C51	EI	VSMI	SMI	0.012
	C52	VSLI	EI	EI
	C53	SLI	EI	EI
Expert 2	C51	EI	SMI	MMI	0.037
	C52	SLI	EI	MLI
	C53	MLI	MMI	EI
Expert 3	C51	EI	VSMI	MMI	0.062
	C52	VSLI	EI	SLI
	C53	MLI	SMI	EI

Expert	Expert 1	Expert 2	Expert 3
Expert 1	1	0.930	0.911
Expert 2	0.930	1	0.976
Expert 3	0.911	0.976	1

Mission capability assessment of UAV swarms based on UAF and interval-valued spherical fuzzy ANP

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With respect to C42	C51	C52	C53	Local weight
C51	([0.45, 0.55], [0.45, 0.55], [0.30, 0.40])	([0.68, 0.79], [0.24, 0.33], [0.18, 0.24])	([0.48, 0.58], [0.42, 0.52], [0.28, 0.37])	([0.56, 0.66], [0.36, 0.46], [0.25, 0.35])
C52	([0.15, 0.28], [0.73, 0.85], [0.16, 0.22])	([0.45, 0.55], [0.45, 0.55], [0.30, 0.40])	([0.35, 0.45], [0.55, 0.65], [0.25, 0.30])	([0.35, 0.45], [0.57, 0.67], [0.25, 0.34])
C53	([0.41, 0.51], [0.49, 0.59], [0.28, 0.36])	([0.55, 0.65], [0.35, 0.45], [0.25, 0.30])	([0.45, 0.55], [0.45, 0.55], [0.30, 0.40])	([0.48, 0.58], [0.43, 0.53], [0.28, 0.37])

Criterion		C1			C2			C3		C4		C5
Criterion		C11	C12	C13	C21	C22	C23	C31	C32	C41	C42	C51	C52	C53
C1	C11	0	0	0	0	0	1	0	0	0	0	0	0	0
	C12	0	0	0	0	0	0	0	0	1	0	0	0	0
	C13	0	0	0	0	0	0	1	0	0	0	0	0	0
C2	C21	0	0	0.5839	0	0	0	0	0	0	0	0	0	0
	C22	0	0	0	0.4483	0	0	0	0	0	0	0	0.5668	0
	C23	1	0	0.4161	0.5517	0	0	0	0	0	0	0	0.4332	0
C3	C31	0	0	0	0	0	0	0	0	0	0	0	0.4970	0
C3	C32	0	0	0	0	0	0	0	0	0	0	0	0.5030	0
C4	C41	0.4623	0	0	1	0	0	1	0	0	0	0	0	0
C4	C42	0.5377	1	1	0	0	0	0	0	0	0	0	0	0
C5	C51	0.3818	0	0	0	0	0	0.4137	0.2805	0.4278	0.4008	0	0	0
	C52	0.2722	0	0	0	0	0	0.3090	0.3802	0.2531	0.2535	0	0	0
	C53	0.3460	0	0	0	0	0	0.2773	0.3393	0.3191	0.3458	0	0	0

Capability	C1	C2	C3	C4	C5
C1	0	0.4034	0.3397	0.5347	0
C2	0.3393	0.2595	0	0	0.5980
C3	0	0	0	0	0.4020
C4	0.3716	0.3371	0.3680	0	0
C5	0.2891	0	0.2923	0.4653	0

Capability	Sub-capability	Global weight
C1	C11	0.1787
	C12	0.0467
	C13	0.0128
C2	C21	0.0051
	C22	0.0465
	C23	0.1259
C3	C31	0.0266
C3	C32	0.0269
C4	C41	0.0615
C4	C42	0.1265
C5	C51	0.1326
	C52	0.0937
	C53	0.1165

Sub-capability	S1	S2	S3	S4	S5
C11	1.0000	0.3544	0.9346	0.1571	0.0254
C12	0.8767	0.3262	0.6597	0.1693	0.0139
C13	0.0064	0.1091	0.9509	1.0000	0.3902
C21	0.9998	0.7684	0.4969	0.2053	0.6415
C22	0.6622	0.2000	0.9615	1.0000	0.0082
C23	0.5766	0.1458	0.6476	0.0029	0.7639
C31	0.3289	0.1147	0.8521	1.0000	0.0021
C32	1.0000	1.0000	0.9970	0.9664	0.8876
C41	1.0000	1.0000	0.8621	0.0000	0.8000
C42	0.9262	0.9692	0.0000	0.4605	0.0296
C51	1.0000	0.0023	0.0069	0.3678	0.1301
C52	0.5000	0.9878	0.1552	0.0302	0.1000
C53	0.0000	0.7903	1.0000	1.0000	0.3817

Method	S1	S2	S3	S4	S5
ANP	0.7727	0.4431	0.5405	0.3384	0.2456
FANP	0.7600	0.4736	0.5434	0.3552	0.2472
SF-ANP	0.7439	0.5076	0.5455	0.3997	0.2609
IVSF-ANP	0.7220	0.5105	0.5732	0.3756	0.2580

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