A novel risk ranking method based on the single valued neutrosophic set

Kuei-Hu Chang

doi:10.3934/jimo.2021065

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doi: 10.3934/jimo.2021065

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A novel risk ranking method based on the single valued neutrosophic set

Kuei-Hu Chang ^,

Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan, Institute of Innovation and Circular Economy, Asia University, Taichung 413, Taiwan

^* Corresponding author: Kuei-Hu Chang

Received February 2020 Revised January 2021 Early access April 2021

Fund Project: The research is supported by the Ministry of Science and Technology, Taiwan(Grant No. MOST 107-2410-H-145-001, MOST 108-2410-H-145-001, and MOST 109-2410-H-145-002)

Risk assessment is a key issue in the process of product design and manufacturing. Traditionally risk assessment uses the risk priority number (RPN) method to rank the extent of a threat. However, this simultaneously includes quantitative and qualitative evaluation factors in the process of risk assessment. Moreover, the information provided by different experts for evaluation factors contain ambiguous, incomplete and inconsistent information. These problems lead to more difficulty for risk assessment, and cannot be effectively solved by the traditional RPN method. To solve some limits of the traditional risk analysis method, this paper integrates the single valued neutrosophic set and subsethood measure method to rank the extent of the threat. For missing or incomplete information in the information aggregation process, the minimum, averaging and maximum operators are used to perform data imputation to avoid the distortion of decision results. Finally, a numerical example of high-dose-rate (HDR) brachytherapy treatments is provided to demonstrate the effectiveness and feasibility of the proposed method, and a comparative analysis with some other existing methods is given.

Keywords: Risk assessment, neutrosophic set, single valued neutrosophic set, multi-criteria decision-making.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Kuei-Hu Chang. A novel risk ranking method based on the single valued neutrosophic set. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021065

References:

[1]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87-96. doi: 10.1016/S0165-0114(86)80034-3. Google Scholar
[2]	P. Biswas, S. Pramanik and B. C. Giri, TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Comput. Appl., 27 (2016), 727-737. doi: 10.1007/s00521-015-1891-2. Google Scholar
[3]	British Standards Institute, Reliability of Systems, Equipment and Components, Guide to Failure Modes, Effects and Criticality Analysis (FMEA and FMECA), Vol. BS 5760-5, British Standards Institute, United Kingdom, 1991. Google Scholar
[4]	K. H. Chang, Evaluate the orderings of risk for failure problems using a more general RPN methodology, Microelectron. Reliab., 49 (2009), 1586-1596. doi: 10.1016/j.microrel.2009.07.057. Google Scholar
[5]	K. H. Chang, A novel reliability calculation method under neutrosophic environments, Ann. Oper. Res., (2021) in press. doi: 10.1007/s10479-020-03890-4. Google Scholar
[6]	K. H. Chang, A more general risk assessment methodology using soft sets based ranking technique, Soft Comput., 18 (2014), 169-183. doi: 10.1007/s00500-013-1045-3. Google Scholar
[7]	K. H. Chang, Y. C. Chang and P. T. Lai, Applying the concept of exponential approach to enhance the assessment capability of FMEA, J. Intell. Manuf., 25 (2014), 1413-1427. doi: 10.1007/s10845-013-0747-9. Google Scholar
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[9]	N. Chanamool and T. Naenna, Fuzzy FMEA application to improve decision-making process in an emergency department, Appl. Soft. Comput., 43 (2016), 441-453. doi: 10.1016/j.asoc.2016.01.007. Google Scholar
[10]	K. H. Chang, Generalized multi-attribute failure mode analysis, Neurocomputing, 175 (2016), 90-100. doi: 10.1016/j.neucom.2015.10.039. Google Scholar
[11]	D.C. US Department of Defense Washington, Procedures for Performing a Failure Mode Effects and Criticality Analysis, US MIL-STD-1629A, 1980. Google Scholar
[12]	M. Giardina, F. Castiglia and E. Tomarchio, Risk assessment of component failure modes and human errors using a new FMECA approach: Application in the safety analysis of HDR brachytherapy, J. Radiol. Prot., 34 (2014), 891-914. doi: 10.1088/0952-4746/34/4/891. Google Scholar
[13]	Y. H. Guo and A. Sengur, A novel 3D skeleton algorithm based on neutrosophic cost function, Appl. Soft. Comput., 36 (2015), 210-217. doi: 10.1016/j.asoc.2015.07.025. Google Scholar
[14]	International Electrotechnical Commission, Analysis Techniques for System Reliability- Procedures for Failure Mode and Effect Analysis, Geneva, IEC 60812, 1985. Google Scholar
[15]	H. A. Khorshidi, I. Gunawan and M. Y. Ibrahim, Applying UGF concept to enhance the assessment capability of FMEA, Qual. Reliab. Eng. Int., 32 (2016), 1085-1093. doi: 10.1002/qre.1817. Google Scholar
[16]	P. Kraipeerapun and C. C. Fung, Binary classification using ensemble neural networks and interval neutrosophic sets, Neurocomputing, 72 (2009), 2845-2856. doi: 10.1016/j.neucom.2008.07.017. Google Scholar
[17]	S. Li and W. Zeng, Risk analysis for the supplier selection problem using failure modes and effects analysis (FMEA), J. Intell. Manuf., 27 (2016), 1309-1321. doi: 10.1007/s10845-014-0953-0. Google Scholar
[18]	H. C. Liu, J. X. You, X. J. Fan and Q. L. Lin, Failure mode and effects analysis using D numbers and grey relational projection method, Expert Syst. Appl., 41 (2014), 4670-4679. doi: 10.1016/j.eswa.2014.01.031. Google Scholar
[19]	O. Mohsen and N. Fereshteh, An extended VIKOR method based on entropy measure for the failure modes risk assessment - A case study of the geothermal power plant (GPP), Saf. Sci., 92 (2017), 160-172. doi: 10.1016/j.ssci.2016.10.006. Google Scholar
[20]	H. Safari, Z. Faraji and S. Majidian, Identifying and evaluating enterprise architecture risks using FMEA and fuzzy VIKOR differentiables, J. Intell. Manuf., 27 (2016), 475-486. doi: 10.1007/s10845-014-0880-0. Google Scholar
[21]	R. Sahin and P. D. Liu, Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information, Neural Comput. Appl., 27 (2016), 2017-2029. doi: 10.1007/s10700-006-0022-z. Google Scholar
[22]	R. Sahin and A. Kucuk, Subsethood measure for single valued neutrosophic sets, J. Intell. Fuzzy Syst., 29 (2015), 525-530. doi: 10.3233/ifs-141304. Google Scholar
[23]	F. Smarandache, A unifying field in logics, neutrosophy: Neutrosophic probability, set and logic, preprint, arXiv: 0101228. Google Scholar
[24]	Z. P. Tian, H. Y. Zhang, J. Wang, J. Q. Wang and X. H. Chen, Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets, Int. J. Syst. Sci., 47 (2016), 3598-3608. doi: 10.1080/00207721.2015.1102359. Google Scholar
[25]	H. Wang, F. Smarandache, Y. Q. Zhang and R. Sunderraman, Single valued neutrosophic sets, Multispace Multistructure, 4 (2014), 410-413. doi: 10.1007/s00357-017-9225-y. Google Scholar
[26]	J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., 26 (2014), 2459-2466. doi: 10.3233/IFS-130916. Google Scholar
[27]	J. Ye, Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, J. Intell. Fuzzy Syst., 26 (2014), 165-172. doi: 10.3233/IFS-130916. Google Scholar
[28]	J. Ye, Multicriteria decision-making method using the correlation coefficient under single-value neutrosophic environment, J. Intell. Fuzzy Syst., 42 (2013), 386-394. doi: 10.1080/03081079.2012.761609. Google Scholar
[29]	L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X. Google Scholar
[30]	E. K. Zavadskas, R. Bausys and M. Lazauskas, Sustainable assessment of alternative sites for the construction of a waste incineration plant by applying WASPAS method with single-valued neutrosophic set, Sustainability, 7 (2015), 15923-15936. doi: 10.3390/su71215792. Google Scholar
[31]	H. Y. Zhang, J. Q. Wang and X. H. Chen, Interval neutrosophic sets and their application in multicriteria decision making problems, Sci. World J., 2014 (2014), Article ID 645953. doi: 10.1155/2014/645953. Google Scholar
[32]	J. H. Zhao, X. Wang, H. M. Zhang, J. Hu and X. M. Jian, Side scan sonar image segmentation based on neutrosophic set and quantum-behaved particle swarm optimization algorithm, Mar. Geophys. Res., 37 (2016), 229-241. doi: 10.1007/s11001-016-9276-1. Google Scholar

show all references

References:

[1]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87-96. doi: 10.1016/S0165-0114(86)80034-3. Google Scholar
[2]	P. Biswas, S. Pramanik and B. C. Giri, TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Comput. Appl., 27 (2016), 727-737. doi: 10.1007/s00521-015-1891-2. Google Scholar
[3]	British Standards Institute, Reliability of Systems, Equipment and Components, Guide to Failure Modes, Effects and Criticality Analysis (FMEA and FMECA), Vol. BS 5760-5, British Standards Institute, United Kingdom, 1991. Google Scholar
[4]	K. H. Chang, Evaluate the orderings of risk for failure problems using a more general RPN methodology, Microelectron. Reliab., 49 (2009), 1586-1596. doi: 10.1016/j.microrel.2009.07.057. Google Scholar
[5]	K. H. Chang, A novel reliability calculation method under neutrosophic environments, Ann. Oper. Res., (2021) in press. doi: 10.1007/s10479-020-03890-4. Google Scholar
[6]	K. H. Chang, A more general risk assessment methodology using soft sets based ranking technique, Soft Comput., 18 (2014), 169-183. doi: 10.1007/s00500-013-1045-3. Google Scholar
[7]	K. H. Chang, Y. C. Chang and P. T. Lai, Applying the concept of exponential approach to enhance the assessment capability of FMEA, J. Intell. Manuf., 25 (2014), 1413-1427. doi: 10.1007/s10845-013-0747-9. Google Scholar
[8]	Y. C. Chang, K. H. Chang and C. Y. Chen, Risk assessment by quantifying and prioritizing 5S activity for semiconductor manufacturing, Proc. Inst. Mech. Eng. Part B-J. Eng. Manuf., 227 (2013), 1874-1887. doi: 10.1177/0954405413493901. Google Scholar
[9]	N. Chanamool and T. Naenna, Fuzzy FMEA application to improve decision-making process in an emergency department, Appl. Soft. Comput., 43 (2016), 441-453. doi: 10.1016/j.asoc.2016.01.007. Google Scholar
[10]	K. H. Chang, Generalized multi-attribute failure mode analysis, Neurocomputing, 175 (2016), 90-100. doi: 10.1016/j.neucom.2015.10.039. Google Scholar
[11]	D.C. US Department of Defense Washington, Procedures for Performing a Failure Mode Effects and Criticality Analysis, US MIL-STD-1629A, 1980. Google Scholar
[12]	M. Giardina, F. Castiglia and E. Tomarchio, Risk assessment of component failure modes and human errors using a new FMECA approach: Application in the safety analysis of HDR brachytherapy, J. Radiol. Prot., 34 (2014), 891-914. doi: 10.1088/0952-4746/34/4/891. Google Scholar
[13]	Y. H. Guo and A. Sengur, A novel 3D skeleton algorithm based on neutrosophic cost function, Appl. Soft. Comput., 36 (2015), 210-217. doi: 10.1016/j.asoc.2015.07.025. Google Scholar
[14]	International Electrotechnical Commission, Analysis Techniques for System Reliability- Procedures for Failure Mode and Effect Analysis, Geneva, IEC 60812, 1985. Google Scholar
[15]	H. A. Khorshidi, I. Gunawan and M. Y. Ibrahim, Applying UGF concept to enhance the assessment capability of FMEA, Qual. Reliab. Eng. Int., 32 (2016), 1085-1093. doi: 10.1002/qre.1817. Google Scholar
[16]	P. Kraipeerapun and C. C. Fung, Binary classification using ensemble neural networks and interval neutrosophic sets, Neurocomputing, 72 (2009), 2845-2856. doi: 10.1016/j.neucom.2008.07.017. Google Scholar
[17]	S. Li and W. Zeng, Risk analysis for the supplier selection problem using failure modes and effects analysis (FMEA), J. Intell. Manuf., 27 (2016), 1309-1321. doi: 10.1007/s10845-014-0953-0. Google Scholar
[18]	H. C. Liu, J. X. You, X. J. Fan and Q. L. Lin, Failure mode and effects analysis using D numbers and grey relational projection method, Expert Syst. Appl., 41 (2014), 4670-4679. doi: 10.1016/j.eswa.2014.01.031. Google Scholar
[19]	O. Mohsen and N. Fereshteh, An extended VIKOR method based on entropy measure for the failure modes risk assessment - A case study of the geothermal power plant (GPP), Saf. Sci., 92 (2017), 160-172. doi: 10.1016/j.ssci.2016.10.006. Google Scholar
[20]	H. Safari, Z. Faraji and S. Majidian, Identifying and evaluating enterprise architecture risks using FMEA and fuzzy VIKOR differentiables, J. Intell. Manuf., 27 (2016), 475-486. doi: 10.1007/s10845-014-0880-0. Google Scholar
[21]	R. Sahin and P. D. Liu, Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information, Neural Comput. Appl., 27 (2016), 2017-2029. doi: 10.1007/s10700-006-0022-z. Google Scholar
[22]	R. Sahin and A. Kucuk, Subsethood measure for single valued neutrosophic sets, J. Intell. Fuzzy Syst., 29 (2015), 525-530. doi: 10.3233/ifs-141304. Google Scholar
[23]	F. Smarandache, A unifying field in logics, neutrosophy: Neutrosophic probability, set and logic, preprint, arXiv: 0101228. Google Scholar
[24]	Z. P. Tian, H. Y. Zhang, J. Wang, J. Q. Wang and X. H. Chen, Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets, Int. J. Syst. Sci., 47 (2016), 3598-3608. doi: 10.1080/00207721.2015.1102359. Google Scholar
[25]	H. Wang, F. Smarandache, Y. Q. Zhang and R. Sunderraman, Single valued neutrosophic sets, Multispace Multistructure, 4 (2014), 410-413. doi: 10.1007/s00357-017-9225-y. Google Scholar
[26]	J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., 26 (2014), 2459-2466. doi: 10.3233/IFS-130916. Google Scholar
[27]	J. Ye, Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, J. Intell. Fuzzy Syst., 26 (2014), 165-172. doi: 10.3233/IFS-130916. Google Scholar
[28]	J. Ye, Multicriteria decision-making method using the correlation coefficient under single-value neutrosophic environment, J. Intell. Fuzzy Syst., 42 (2013), 386-394. doi: 10.1080/03081079.2012.761609. Google Scholar
[29]	L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X. Google Scholar
[30]	E. K. Zavadskas, R. Bausys and M. Lazauskas, Sustainable assessment of alternative sites for the construction of a waste incineration plant by applying WASPAS method with single-valued neutrosophic set, Sustainability, 7 (2015), 15923-15936. doi: 10.3390/su71215792. Google Scholar
[31]	H. Y. Zhang, J. Q. Wang and X. H. Chen, Interval neutrosophic sets and their application in multicriteria decision making problems, Sci. World J., 2014 (2014), Article ID 645953. doi: 10.1155/2014/645953. Google Scholar
[32]	J. H. Zhao, X. Wang, H. M. Zhang, J. Hu and X. M. Jian, Side scan sonar image segmentation based on neutrosophic set and quantum-behaved particle swarm optimization algorithm, Mar. Geophys. Res., 37 (2016), 229-241. doi: 10.1007/s11001-016-9276-1. Google Scholar

Table 1. Traditional RPN method scale for severity [18,19]

Rating	Effect	Severity of effect
10	Hazardous without warning	Highest severity ranking of a failure mode, occurring without warning and consequence is hazardous
9	Hazardous with warning	Higher severity ranking of a failure mode occurring with warning, consequence is hazardous
8	Extreme	Operation of system or product is broken down without compromising safe
7	Major	Operation of system or product may be continued but performance of system or product is affected
6	Significant	Operation of system or product is continued and performance of system or product is degraded
5	Moderate	Performance of system or product is affected seriously and the maintenance is needed
4	Low	Performance of system or product is small affected and the maintenance may not be needed
3	Minor	System performance and satisfaction with minor effect
2	Very minor	System performance and satisfaction with slight effect
1	None	No effect

Rating	Probability of failure	Possible failure rates
10	Extremely high: failure almost inevitable	$ \geq $in 2
9	Very high	1 in 3
8	Repeated failures	1 in 8
7	High	1 in 20
6	Moderately high	1 in 80
5	Moderate	1 in 400
4	Relatively low	1 in 2000
3	Low	1 in 15,000
2	Remote	1 in 150,000
1	Nearly impossible	$ \leq $1 in 1,500,000

Rating	Detection	Likelihood of detection by design control
10	Absolute uncertainty	Potential occurring of failure mode cannot be detected in concept, design and process failure mode and effects analysis (FMEA)/mechanism and subsequent failure mode
9	Very remote	The possibility of detecting the potential occurring of failure mode is very remote/mechanism and subsequent failure mode
8	Remote	The possibility of detecting the potential occurring of failure mode is remote/mechanism and subsequent failure mode
7	Very low	The possibility of detecting the potential occurring of failure mode is very low/mechanism and subsequent failure mode
6	Low	The possibility of detecting the potential occurring of failure mode is low/mechanism and subsequent failure mode
5	Moderate	The possibility of detecting the potential occurring of failure mode is moderate/mechanism and subsequent failure mode
4	Moderately high	The possibility of detecting the potential occurring of failure mode is moderately high/mechanism and subsequent failure mode
3	High	The possibility of detecting the potential occurring of failure mode is high/mechanism and subsequent failure mode
2	Very high	The possibility of detecting the potential occurring of failure mode is very high/mechanism and subsequent failure mode
1	Almost certain	The potential occurring of failure mode will be detect/ mechanism and subsequent failure mode

Identification number (ID)	Component	Failure mode	Failure effect
1	Stepping motor	Electrical blackout	High-dose-rate (HDR) unit is stopped and dc motor withdraws the source to the safe
2	Direct current safety motor	Loss of power	Operator goes into the treatment room (TR) to manually return the source to the safe
3	Dwell position distance control device	Stepper motor failure	Source position not correct
4	Secondary timer	Electronic fault	Incorrect check of the primary timer
5	Backup battery	Power-off	Direct current motor fault
6	Backup battery	Operator forgets to charge the battery	Direct current motor fault
7	Software	Power-off	Safety and control system fault
8	Stop button on the console	Contact fault	During treatment, the stop button on the console did not retract the wire source
9	Physicist	Dose calculation errors during treatment planning system (TPS)	Incorrect HDR treatment
10	Therapist	Data insertion errors during TPS	Incorrect HDR treatment
11	Medical operator	Incorrect patient identification	Incorrect data are used during treatment control system (TCS)
12	Medical operator	Incorrect medical application of the catheter or applicator	Incorrect HDR treatment
13	Therapist	Error in loading patient information (from the database)	Incorrect data are used during TCS
14	Therapist	Error in the data entry for dwell time or dwell position programming	Incorrect data are used during TCS

Level	S	O	D	Single valued neutrosophic
10	Hazardous	Extremely high	Absolute uncertainty	(1.00, 0.00, 0.00)
9	Serious	Very high	Very remote	(0.90, 0.10, 0.10)
8	Extreme	Repeated failures	Remote	(0.80, 0.15, 0.20)
7	Major	High	Very low	(0.70, 0.25, 0.30)
6	Significant	Moderately high	Low	(0.60, 0.35, 0.40)
5	Moderate	Moderate	Moderate	(0.50, 0.50, 0.50)
4	Low	Relatively low	Moderately high	(0.40, 0.65, 0.60)
3	Minor	Low	High	(0.30, 0.75, 0.70)
2	Very minor	Remote	Very high	(0.20, 0.85, 0.80)
1	None	Nearly impossible	Almost certain	(0.10, 0.90, 0.90)

ID	S				O				D
ID	TM1	TM2	TM3	TM4	TM1	TM2	TM3	TM4	TM1	TM2	TM3	TM4
1	2	2	1	2	1	1	2	1	10	10	9	10
2	1	1	1	1	10	10	9	9	2	2	1	2
3	1	2	1	1	8	7	8	8	3	2	3	4
4	3	2	3	3	7	7	8	6	2	2	2	3
5	4	4	3	3	9	8	9	9	2	1	2	2
6	3	2	2	3	9	9	9	9	2	2	2	2
7	1	1	2	1	9	8	8	9	9	8	9	9
8	1	1	1	2	10	9	10	10	9	9	9	10
9	4	3	3	5	9	8	8	9	3	2	3	3
10	5	6	4	5	9	9	9	10	2	3	2	2
11	5	5	*	6	9	8	*	9	3	4	*	3
12	2	3	*	2	1	1	*	2	10	9	*	10
13	5	5	4	6	9	10	10	8	2	2	2	3
14	4	4	5	4	9	9	10	9	2	2	1	2
* Missing or incomplete information

ID	S			O			D
1	0.267	0.283	0.267	0.300	0.300	0.300	0.000	0.000	0.000
2	0.300	0.300	0.300	0.000	0.000	0.000	0.267	0.283	0.267
3	0.300	0.300	0.300	0.067	0.050	0.067	0.233	0.250	0.233
4	0.233	0.250	0.233	0.100	0.083	0.100	0.267	0.283	0.267
5	0.200	0.217	0.200	0.033	0.033	0.033	0.267	0.283	0.267
6	0.233	0.250	0.233	0.033	0.033	0.033	0.267	0.283	0.267
7	0.300	0.300	0.300	0.033	0.033	0.033	0.033	0.033	0.033
8	0.300	0.300	0.300	0.000	0.000	0.000	0.033	0.033	0.033
9	0.200	0.217	0.200	0.033	0.033	0.033	0.233	0.250	0.233
10	0.167	0.167	0.167	0.033	0.033	0.033	0.267	0.283	0.267
11	0.167	0.167	0.167	0.033	0.033	0.033	0.233	0.250	0.233
12	0.267	0.283	0.267	0.300	0.300	0.300	0.000	0.000	0.000
13	0.167	0.167	0.167	0.033	0.033	0.033	0.267	0.283	0.267
14	0.200	0.217	0.200	0.033	0.033	0.033	0.267	0.283	0.267

ID	Minimum operator
ID	S			O			D
11	0.50	0.50	0.50	0.80	0.15	0.20	0.30	0.75	0.70
12	0.20	0.85	0.80	0.10	0.90	0.90	0.90	0.10	0.10
	Averaging operator
11	0.536	0.444	0.464	0.874	0.114	0.126	0.335	0.715	0.665
12	0.235	0.815	0.765	0.135	0.883	0.865	1.000	0.000	0.000
	Maximum Operator
11	0.60	0.35	0.40	0.90	0.10	0.10	0.40	0.65	0.60
12	0.30	0.75	0.70	0.20	0.85	0.80	1.00	0.00	0.00

ID	S	O	D
1	(0.18, 0.86, 0.82)	(0.13, 0.89, 0.87)	(1.00, 0.00, 0.00)
2	(0.10, 0.90, 0.90)	(1.00, 0.00, 0.00)	(0.18, 0.86, 0.82)
3	(0.13, 0.89, 0.87)	(0.78, 0.17, 0.22)	(0.30, 0.75, 0.70)
4	(0.28, 0.77, 0.72)	(0.71, 0.24, 0.29)	(0.23, 0.82, 0.77)
5	(0.35, 0.70, 0.65)	(0.88, 0.11, 0.12)	(0.18, 0.86, 0.82)
6	(0.25, 0.80, 0.75)	(0.90, 0.10, 0.10)	(0.20, 0.85, 0.80)
7	(0.13, 0.89, 0.87)	(0.86, 0.12, 0.14)	(0.88, 0.11, 0.12)
8	(0.13, 0.89, 0.87)	(1.00, 0.00, 0.00)	(1.00, 0.00, 0.00)
9	(0.38, 0.65, 0.62)	(0.86, 0.12, 0.14)	(0.28, 0.77, 0.72)
10	(0.51, 0.49, 0.49)	(1.00, 0.00, 0.00)	(0.23, 0.82, 0.77)
11	(0.53, 0.46, 0.47)	(0.86, 0.12, 0.14)	(0.33, 0.72, 0.67)
12	(0.23, 0.82, 0.77)	(0.13, 0.89, 0.87)	(1.00, 0.00, 0.00)
13	(0.51, 0.49, 0.49)	(1.00, 0.00, 0.00)	(0.23, 0.82, 0.77)
14	(0.43, 0.61, 0.57)	(1.00, 0.00, 0.00)	(0.18, 0.86, 0.82)

ID	S			O			D
1	0.275	0.287	0.275	0.291	0.296	0.291	0.000	0.000	0.000
2	0.300	0.300	0.300	0.000	0.000	0.000	0.275	0.287	0.275
3	0.291	0.296	0.291	0.074	0.057	0.074	0.232	0.249	0.232
4	0.241	0.258	0.241	0.097	0.080	0.097	0.258	0.275	0.258
5	0.216	0.233	0.216	0.040	0.037	0.040	0.275	0.287	0.275
6	0.249	0.266	0.249	0.033	0.033	0.033	0.267	0.283	0.267
7	0.291	0.296	0.291	0.047	0.041	0.047	0.040	0.037	0.040
8	0.291	0.296	0.291	0.000	0.000	0.000	0.000	0.000	0.000
9	0.206	0.218	0.206	0.047	0.041	0.047	0.241	0.258	0.241
10	0.165	0.163	0.165	0.000	0.000	0.000	0.258	0.275	0.258
11	0.158	0.152	0.158	0.047	0.041	0.047	0.225	0.241	0.225
12	0.258	0.275	0.258	0.291	0.296	0.291	0.000	0.000	0.000
13	0.165	0.163	0.165	0.000	0.000	0.000	0.258	0.275	0.258
14	0.191	0.203	0.191	0.000	0.000	0.000	0.275	0.287	0.275

ID	S	O	D	RPN ^[4,12]	Ranking RPN ^[4,12]	$S\left(A^{*}, A_{i}\right)$ ^[22]	Ranking subsethood measure ^[22]	$S_{1}(A, B)$ ^[27]	Ranking $S_1(A, B)$ ^[27]	$S_2(A, B)$ ^[27]	Ranking $S_2(A, B)$ ^[27]	$d_H(A, B)$ ^[27]	Ranking $d_H(A, B)$ ^[27]	$d_E(A, B)$ ^[27]	Ranking $d_E(A, B)$ ^[27]
1	2	1	10	20	12	0.806	10	0.865	10	0.449	13	0.572	10	0.702	12
2	1	10	2	20	12	0.806	10	0.865	10	0.475	12	0.572	10	0.702	12
3	1	8	3	24	11	0.794	13	0.856	13	0.514	9	0.600	13	0.673	11
4	3	7	2	42	10	0.789	14	0.854	14	0.485	11	0.606	14	0.649	10
5	4	9	2	72	7	0.822	7	0.885	7	0.520	7	0.511	7	0.594	7
6	3	9	2	54	9	0.811	9	0.874	9	0.508	10	0.544	9	0.630	9
7	1	9	9	81	6	0.878	2	0.933	2	0.755	2	0.367	2	0.526	3
8	1	10	9	90	3	0.889	1	0.944	1	0.762	1	0.333	1	0.523	2
9	4	9	3	108	2	0.833	6	0.896	6	0.576	4	0.478	6	0.549	4
10	5	9	2	90	3	0.839	4	0.898	4	0.525	5	0.472	4	0.556	5
11	5	9	3	135	1	0.850	3	0.909	3	0.582	3	0.439	3	0.508	1
12	2	1	10	20	12	0.806	10	0.865	10	0.449	13	0.572	10	0.702	12
13	5	9	2	90	3	0.839	4	0.898	4	0.525	5	0.472	4	0.556	5
14	4	9	2	72	7	0.822	7	0.885	7	0.520	7	0.511	7	0.594	7

ID	S	O	D	$C(A, B)$ ^[28]	Ranking $C(A, B)$ ^[28]	Proposed method
ID	S	O	D	$C(A, B)$ ^[28]	Ranking $C(A, B)$ ^[28]	Minimum operator	Ranking minimum operator		Averaging operator		Ranking averaging operators		Maximum Operator		Ranking maximum operator
1	2	1	10	0.86	12	0.806	10		0.806		10		0.806		10
2	1	10	2	0.86	12	0.804	12		0.804		12		0.804		12
3	1	8	3	1.05	11	0.794	13		0.794		13		0.794		13
4	3	7	2	1.18	10	0.790	14		0.790		14		0.790		14
5	4	9	2	1.43	7	0.813	8		0.813		8		0.813		9
6	3	9	2	1.21	9	0.806	10		0.806		10		0.806		10
7	1	9	9	1.79	2	0.872	2		0.872		2		0.872		2
8	1	10	9	1.72	3	0.901	1		0.901		1		0.901		1
9	4	9	3	1.69	6	0.826	7		0.826		7		0.826		7
10	5	9	2	1.71	4	0.853	3		0.853		4		0.853		4
11	5	9	3	2.02	1	0.851	5		0.855		3		0.860		3
12	2	1	10	0.86	12	0.810	9		0.811		9		0.814		8
13	5	9	2	1.71	4	0.853	3		0.853		4		0.853		4
14	4	9	2	1.43	7	0.837	6		0.837		6		0.837		6

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A novel risk ranking method based on the single valued neutrosophic set

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