Re-contextualization is basically a transformative process of reframing a system structure to assume that of another system. It extracts texts, symbols, signs, artefacts, or meanings from its original structure to assume another structure in context. The concept is applied in abstract and quantitative fuzziness to resolve and re-interpret discrete fuzzy function by assuming fuzzy polynomial structure. This study is premised upon the fuzziness in relationships exhibited by cyber-security vulnerabilities and threat constructs as fuzzy functions. The evaluation of discrete fuzzy functions based on arbitrary equidistant computations render the solution indeterminate. However, re-contextualizing the cyber-risk function into a fuzzy polynomial simplifies the solution and depicts its functional nature for real world applications. Numerical examples are used to illustrate the concept by the Ranking method.

Cyber-Risk; Re-contextualization; Fuzzy Polynomial; Discrete Fuzzy Functions; Ranking Method

[1] M. Stoner, "Reframing, Recontextualizing and the Social Reconstruction of Higher Education in California, USA.," in ECER 2012 Symposium (Cadiz) Network 23 Policy Studies and Politics fo Education, 2012.
[2] A. Clemons and A. Smith, "Recontextualizing Bloom`s Taxonomy: Quantitative Measures in Formative Curriculum Assessments and Program Evaluation," 2016. [Online]. Available: https://www.academia.edu/22270014/Recontextualizing_Bloom_s_Taxonomy_Quantitative_Measures_in_Formative_Curriculum_Assessments_and_Program_Evaluations . [Accessed 5 August 2016].
[3] B. M. Ayyub, Elicitation of Expert Opinions for Uncertainty & Risks, CRC Press LLC, 2001.
[4] I. Perfilieva, "Fuzzy Function: Theoretical and Practical Point of View," in EUSFLAT, Aix-les-Bains, France, 2011.
[5] L. Zadeh, "The Concept of a Liinguistic Variable and Its Application to Approximate Reasoning," Information Sciences, vol. 8, pp. 199-257, 1975.
[6] B. Moller and U. Reuter, Uncertainty Forecasting in Engineering, Berlin: Springer, 2007.
[7] E. O. Yeboah-Boateng, "Cyber-Security Challenges with SMEs in Developing Economies: Issues of Confidentiality, Integrity & Availablity (CIA)," center for Communications, Media & Information technologies (CMI), Aalborg University, Copengahen, 2013a.
[8] J. L. Darby, "Estimating Terrorist Risk with Possibility Theory," Los Alamos National Laboratory, USA, 2004.
[9] N. Ye, Secure Computer & Network Systems: Modeling, Analysis & Design, John Wiley & Sons, 2008.
[10] S. K. Katsikas, "Risk Management," in Computer & Information Security Handbook, Morgan-Kaufmann, Inc., 2009, pp. 605-625.
[11] M. Hanss, Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer, 2005.
[12] C. W. Cook, A. J. Hickle and E. M. Ruchensky, "Fuzzy One-Dimensional Models," in Applying Fuzzy Mathematics to Formal Models in Comparative Politics, Berlin Heidelberg, Springer-Verlag, 2008, pp. 81-108.
[13] L. Zadeh, "Fuzzy Sets," Information & Control, vol. 8, pp. 338-353, 1965.
[14] H. Kwakemaak, "Fuzzy Random Variables: Definitions and Theorems," Information Science, vol. 15, pp. 1-29, 1978.
[15] M. Yang and M. Liu, "On Possibility Analysis of Fuzzy Data," Fuzzy Sets & Systems, vol. 94, pp. 174-183, 1998.
[16] R. Kruse and K. Meyer, Statistics with Vague Data, Reidel: Dordrecht, 1987.
[17] S.-Y. Wang and C.-C. Hwang, "An Application of Fuzzy Set Theory to the Weighted Average Cost of Capital and Capital Structure Decision," Technology & Investment, vol. 1, no. 4, pp. 248-256, November 2010.
[18] E. Cox, The Fuzzy Systems Handbook: A Practioner`s Guide to Building, Using & Maintaining Fuzzy Systems, Academic Press, Inc., 1994.
[19] P. Dadone, Introduction to Fuzzy Sets, 1995 ed., vol. 83, J. Mendel, Ed., Proceedings of IEEE, 2000.
[20] K. H. Lee, First Course on Fuzzy Theory & Applications, Verlag-Berlin Heidelberg: Springer, 2006.
[21] D. A. Maces and M. A. Stadtherr, "Computing Fuzzy Trajectories for Nonlinear Dynamic Systems," Department of Chemical and Biomedical Engineering, University of Notre Dame, 2013.
[22] J. Buckley and E. Eslami, "Neural Net Solution of Fuzzy Problems: The Quadratic Equation," Fuzzy Sets and Systems, vol. 86, pp. 289-298, 1997.
[23] M. Otadi and M. Mosleh, "Solution of Fuzzy Polynomial Equations by Modified Adomain Decomposition Method," Soft Computing, vol. 15, pp. 187-192, 2011.
[24] S. Abbasbandy and B. Asady, "Newton`s Method for Solving Fuzzy Nonlinear Equations," Applied Mathematics and Computaion, vol. 159, pp. 356-379, 2004.
[25] A. Sala and C. Arino, "Polynomial Fuzzy Models for Nonlinear Control: A Taylor-series Approach," IEEE Transactions on Fuzzy Systems, vol. 17, no. 6, 2010.
[26] S. Abbasbandy and M. Otadi, "Numerical Solution of Fuzzy Polynomials by Fuzzy Neural Network," Applied Mathematics and Computation, vol. 181, pp. 1084-1089, 2006.
[27] N. A. Rahman and L. Abdullah, "Multi-Solutions of Fuzzy Polynomials: A Review," International Journal of Engineering and Applied Sciences, vol. 3, no. 3, pp. 8-16, 2013.
[28] H. Kharrati, S. Khanmohammadi, W. Pedrycz and G. Alizadeh, "Imporved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems," Mathematical Problems in Engineering, vol. 2012, no. 273631, 2012.
[29] H. Rouhparvar, "Solving Fuzzy Polynomial Equation by Ranking Method," in First Joint Congress on Fuzzy and Intelligent Systems, Mashhad, Iran, 2007.
[30] Learning Research and Development Center;, "A Performance-Based Assessment: A Means to High-Level Thinking and Reasoning," University of Pittsburgh, 2012.
[31] C. R. Haugen, "Contextualizations and Recontextualizations of Discourse on Equity in Education," NTNU, 2009.
[32] P. Dowling, The Sociology of Mathematics Education: Mathematical Myths/Pedagogic Texts, Routledge, 2002.
[33] B. Bernstein, Class, Codes, and Control, vol. 4, Routledge, New York: London Routledge & Kegan Paul, 2003.
[34] J. Wu, S. Huang and R. Zheng, "Recontextualization and Transformation in Media Discourse: An Analysis of the First Instance Judgment of the Peng Yu Case," Discourse & Society, 2016.
[35] D. Armstrong, D. Espling, J. Tordsson, K. Djemame and E. Elmroth, "Runtime Virtual Machine Recontextualization for Clouds," in Euro-Par`12 Proceedings of the 18th International Conference on Parallel Processing Workshops, 2012.
[36] H. M. Nehi, "A New Ranking Method for Intuitionistic Fuzzy Numbers," International Journal of Fuzzy Systems, vol. 12, no. 1, 2010.
[37] M. Dondo, A Fuzzy Risk Calculations Approach for a Network Vulnerability Ranking System, 2007.
[38] D. Denning, "Cyber-Security as an Emergent Infrastructure," in Bombs & Bandwidth: The Emerging Relationship between IT & Security, The New Press, 2003.
[39] M. Spivak, Calculus, Texas: Publish or Perish, Inc., 2008.