An application of fuzzy logistic regression for predicting CVSS severity category of industrial control systems

Open Access

Issue		RAIRO-Oper. Res. Volume 56, Number 6, November-December 2022


Page(s)		4083 - 4111
DOI		https://doi.org/10.1051/ro/2022189
Published online		29 November 2022

IBM, What is Industry 4.0? IBM. https://www.ibm.com/topics/industry-4-0 (accessed 21.12.2021, 2021). [Google Scholar]
U.S. Department of Commerce, Information Security. [Online] Available: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-30r1.pdf (2012). [Google Scholar]
U.S. Department of Commerce, Computer Security. [Online] Available: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-30.pdf (2002). [Google Scholar]
National Institute of Standards and Technology (NIST), Vulnerabilities. https://nvd.nist.gov/vuln (accessed 19.06.2021, 2021). [Google Scholar]
D. Braue, Global Cybersecurity Spending to Exceed $1.75 Trillion from 2021 to 2025. https://cybersecurityventures.com/cybersecurity-spending-2021-2025/ (accessed 21.12.2021, 2021). [Google Scholar]
U.S. Department of Commerce, National Institute of Standards and Technology (NIST), National Vulnerability Database. NIST. https://nvd.nist.gov/vuln/data-feeds (accessed 23.12.2021, 2021). [Google Scholar]
U.S. Department of Commerce, National Institute of Standards and Technology (NIST), CVSS Vulnerability Metrics. https://nvd.nist.gov/vuln-metrics/cvss (accessed 22.12.2021, 2021). [Google Scholar]
Cybersecurity & Infrastructure Security Agency, ICS-CERT Advisories. US Department of Homeland Security. https://www.cisa.gov/uscert/ics/advisories (accessed 23.12.2021, 2021). [Google Scholar]
S. Pourahmad, S.M.T. Ayatollahi, S.M. Taheri and Z.H. Agahi, Fuzzy logistic regression based on the least squares approach with application in clinical studies. Comput. Math. App. 62 (2011) 3353–3365. [Google Scholar]
N. Chukhrova and A. Johannssen, Fuzzy regression analysis: systematic review and bibliography. Appl. Soft Comput. 84 (2019) 105708. [CrossRef] [Google Scholar]
FIRST.org, Common Vulnerability Scoring System version 3.1: Specification Document. https://www.first.org/cvss/specification-document (accessed 22.12.2021, 2021). [Google Scholar]
M.G. Dondo, A vulnerability prioritization system using a fuzzy risk analysis approach. in Proceedings of the IFIP Tc 11 23rd International Information Security Conference. Springer US, Boston, MA (2008) 525–540. [Google Scholar]
I.V. Anikin, Using fuzzy logic for vulnerability assessment in telecommunication network, in 2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE (2017) 1–4. DOI: 10.1109/ICIEAM.2017.8076444. [Google Scholar]
K. Gencer and F. Başçiftçi, The fuzzy common vulnerability scoring system (F-CVSS) based on a least squares approach with fuzzy logistic regression. Egypt. Inf. J. 22 (2021) 145–153. [Google Scholar]
Y. Gao and Q. Lu, A fuzzy logistic regression model based on the least squares estimation. Comput. Appl. Math. 37 (2018) 3562–3579. [CrossRef] [MathSciNet] [Google Scholar]
S. Pourahmad, S.M.T. Ayatollahi and S.M. Taheri, Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status. Iran. J. Fuzzy Syst. 8 (2011) 1–17. [MathSciNet] [Google Scholar]
S. Mustafa, S. Asghar and M. Hanif, Fuzzy logistic regression based on least square approach and trapezoidal membership function. Iran. J. Fuzzy Syst. 15 (2018) 97–106. [Google Scholar]
H. Tanaka, S. Uejima and K. Asai, Linear regression analysis with fuzzy model. IEEE Trans. Syst. Man Cybern. 12 (1982) 903–907. [CrossRef] [Google Scholar]
N.Y. Pehlivan and A. Yonar, An integrated approach for fuzzy logistic regression. Istatistikçiler Dergisi: Istatistik ve Aktüerya 11 (2018) 42–54. [Google Scholar]
P. Diamond, Fuzzy least squares. Inf. Sci. 46 (1988) 141–157. [CrossRef] [Google Scholar]
S.Y. Sohn, D.H. Kim and J.H. Yoon, Technology credit scoring model with fuzzy logistic regression. Appl. Soft Comput. 43 (2016) 150–158. [CrossRef] [Google Scholar]
J.H. Yoon and S.H. Choi, Fuzzy least squares estimation with new fuzzy operations, in Synergies of Soft Computing and Statistics for Intelligent Data Analysis, edited by R. Kruse, M.R. Berthold, C. Moewes, M.Á. Gil, P. Grzegorzewski and O. Hryniewicz. Springer Berlin Heidelberg, Berlin, Heidelberg (2013) 193–202. [CrossRef] [Google Scholar]
J.H. Yoon and P. Grzegorzewski, On optimal and asymptotic properties of a fuzzy L2 estimator. Mathematics 8 (2020) 1956. [CrossRef] [Google Scholar]
S.M. Taheri and M. Kelkinnama, Fuzzy least absolutes regression, in 2008 4th International IEEE Conference Intelligent Systems. Vol. 2. IEEE (2008). DOI: 10.1109/IS.2008.4670509. [Google Scholar]
G. Atalik and S. Senturk, A new approach for parameter estimation in fuzzy logistic regression. Iran. J. Fuzzy Syst. 15 (2018) 91–102. [MathSciNet] [Google Scholar]
M. Namdari, A. Abadi, S.M. Taheri, M. Rezaei, N. Kalantari and N. Omidvar, Effect of folic acid on appetite in children: ordinal logistic and fuzzy logistic regressions. Nutrition 30 (2014) 274–278. [CrossRef] [PubMed] [Google Scholar]
M. Namdari, J. Yoon, A. Abadi, S.M. Taheri and S. Choi, Fuzzy logistic regression with least absolute deviations estimators. Soft Comput. 19 (2015) 909–917. [CrossRef] [Google Scholar]
B. Kim and R.R. Bishu, Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst. 100 (1998) 343–352. [CrossRef] [Google Scholar]
F. Salmani, S.M. Taheri and A. Abadi, A forward variable selection method for fuzzy logistic regression. Int. J. Fuzzy Syst. 21 (2019) 1259–1269. [CrossRef] [MathSciNet] [Google Scholar]
R. Xu and C. Li, Multidimensional least-squares fitting with a fuzzy model (in English). Fuzzy Sets Syst. 119 (2001) 215–223. [CrossRef] [Google Scholar]
F. Salmani, S.M. Taheri, J.H. Yoon, A. Abadi, H. Alavi Majd and A. Abbaszadeh, Logistic regression for fuzzy covariates: modeling, inference, and applications. Int. J. Fuzzy Syst. 19 (2017) 1635–1644. [CrossRef] [MathSciNet] [Google Scholar]
R. Nikbakht and A. Bahrampour, Determining factors influencing survival of breast cancer by fuzzy logistic regression model (in English). J. Res. Med. Sci. 22 (2017) 135–135. [CrossRef] [PubMed] [Google Scholar]
A. Behnampour, A. Biglarian and E. Bakhshi, Application of fuzzy logistic regression in modeling the severity of autism spectrum disorder (in English). Jorjani Biomed. J. 7 (2019) 49–60. [CrossRef] [Google Scholar]
M. Kelkinnama and S.M. Taheri, Fuzzy least-absolutes regression using shape preserving operations. Inf. Sci. 214 (2012) 105–120. [CrossRef] [Google Scholar]
T.M.B. Bennaser, Fuzzy logistic regression for detecting differential DNA methylation regions, Ph.D. in Applied Mathematics Doctoral Dissertations, Mathematics and Statistics, Missouri University of Science and Technology, USA (2020). [Google Scholar]
W. Anggraeni, S. Sumpeno, E.M. Yuniarno, R.F. Rachmadi, A.B. Gumelar and M.H. Purnomo, Prediction of dengue fever outbreak based on climate factors using fuzzy-logistic regression, in 2020 International Seminar on Intelligent Technology and its Applications (ISITIA), 22–23 July 2020. IEEE (2020) 199–204. DOI: 10.1109/ISITIA49792.2020.9163708. [CrossRef] [Google Scholar]
L.A. Zadeh, Fuzzy sets. Inf. Control 8 (1965) 338–353. [Google Scholar]
E. Çeven and Ö. Özdemir, Using fuzzy logic to evaluate and predict Chenille Yarn’s shrinkage behaviour. Fibres Text. Eastern Eur. 15 (2007) 55–59. [Google Scholar]
A.H. Gandomi, X.-S. Yang, S. Talatahari and A. Alavi, Metaheuristic algorithms in modeling and optimization, in Metaheuristic Applications in Structures and Infrastructures. Elsevier, London (2013) 1–24. [Google Scholar]
L. Bianchi, M. Dorigo, L.M. Gambardella and W.J. Gutjahr, A survey on metaheuristics for stochastic combinatorial optimization. Nat. Comput. 8 (2009) 239–287. [CrossRef] [MathSciNet] [Google Scholar]
F.A. Hashim, K. Hussain, E.H. Houssein, M.S. Mabrouk and W. Al-Atabany, Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl. Intell. 51 (2021) 1531–1551. [CrossRef] [Google Scholar]
H. Rajabi Moshtaghi, A. Toloie Eshlaghy and M.R. Motadel, A comprehensive review on meta-heuristic algorithms and their classification with novel approach (in English). J. Appl. Res. Ind. Eng. 8 (2021) 63–89. [Google Scholar]
M. Voskoglou, Use of the triangular fuzzy numbers for student assessment. Am. J. Appl. Math. Stat.. Preprint arXiv:1507.03257 (2015). [Google Scholar]
FIRST.org, Common Vulnerability Scoring System v3.0: Specification Document. FIRST https://www.first.org/cvss/v3.0/specification-document#n3 (accessed 26.12.2021, 2021). [Google Scholar]
F. Solvers, Excel solver – change options for evolutionary solving method. Frontline Solvers. https://www.solver.com/excel-solver-change-options-evolutionary-solving-method (accessed 27.12.2021, 2021). [Google Scholar]
CRAN, Package “GenSA”. https://cran.r-project.org/web/packages/GenSA/GenSA.pdf (accessed 27.12.2021, 2021). [Google Scholar]

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