Algorithms for assessing the qualitative and quantitative risks of lending to small and medium-sized businesses based on Fuzzy calculus
Abstract
Today, crisis conditions in the economy and finance require high-quality risk assessment. In the article, the authors propose two algorithms for assessing the projects lending risks (PLRs) to small and medium-sized businesses. To assess qualitative PLRs, we proposed to use a hierarchical system of criteria, in which the importance of the criteria is described using the Sugeno fuzzy measure, and the generalized estimate of the qualitative risk is calculated using the Sugeno fuzzy integral. To evaluate quantitative PLRs, we proposed to use the characteristics of fuzzy numbers that describe the project effectiveness criteria and have an arbitrary-form membership function. In addition, to describe quantitative risks, we proposed to use the risk-function of a fuzzy number, which reflects not only the size of possible losses, but also the possibility of their occurrence. This allows you to comprehensively and objectively assess the level of risks. We have demonstrated and discussed this algorithms on the example of preparing data for making a decision on lending to a project for the production of corn syrup in Ukraine.
References
Appadoo, S.S., Bhatt, S.K., & Bector, C.R. (2008). Application of possibility theory to investment decisions. Fuzzy Optimization and Decision Making, 7 (1), 35-57.
Atra, R.J., & Thomas, R. (2009). Developing an Automated Discounted Cash Flow Model. Thomas, R., Gup, B.E. (eds), The Valuation Handbook, John Wiley & Sons, Inc. 108-134.
Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., Silov, V.B., & Tarasov, V.B. (1986). Fuzzy Sets in Control Models and Artificial Intelligence (in Russian). Pospelov, D.A. (ed). The science, Moscow.
Ayyub, B.M., & Klir, G.J. (2006). Uncertainty Modeling and Analysis in Engineering and the Sciences (1st ed.). Chapman and Hall/CRC.
Bede, B., & Fodor, J. (2006). Product Type Operations between Fuzzy Numbers and their Applications in Geology. Acta Polytechnica Hungarica, 3 (1), 123-139.
Bodjanova, S. (2005). Median value and median interval of a fuzzy number. Information Sciences, 172(1-2), 73–89.
Choquet, G. (1954). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.
Frei, D., & Ruloff, D. (1988). The methodology of political risk assessment: An overview. World Futures: Journal of General Evolution, 25 (1-2), 1-24.
Fuzzy for Excel. Available at: https://www.dropbox.com/s/2qre4sfuo3jawie/Fuzzy%20for%20Excel%2064bit.zip?dl=0
Gejirifu, D., Zhongfu, T., Menglu, L., Lilin H., Qiang W., & Huanhuan L. (2019). A credit risk evaluation based on intuitionistic fuzzy set theory for the sustainable development of electricity retailing companies in China. Energy Science & Engineering, 7 (6), 2825-2841.
Ghatasheh, N. (2014). Business analytics using random forest trees for credit risk prediction: a comparison study. International Journal of Advanced Science and Technology, 72, 19-30.
Liu, H., & Sizong, G.U.O. (2007). Equality and Identity of Fuzzy Numbers and Fuzzy Arithmetic with Equality Constraints. In International Conference on Intelligent Systems and Knowledge Engineering 2007, Atlantis Press. 334-339.
Harrington, E.C. (1965). The Desirability Function. Industrial Quality Control, 21(10), 494 – 498.
Jaya Y, B.J., & Tamilselvi, J.J. (2018). Fuzzy multi-criteria random seed and cutoff point approach for credit risk assessment. Journal of Theoretical & Applied Information Technology, 96 (4), 1150-1163.
Kaufmann, S., Condoravdi, C., & Harizanov, V. (2006) Formal approaches to modality. Frawley, W. (Ed.). The Expression of Modality. Mouton de Gruyter. Berlin, New York. 71-106.
Kengatharan, L. (2016). Capital budgeting theory and practice: a review and agenda for future research. Research Journal of Finance and Accounting, 7 (1), 1-22.
Keshk, A.M., Maarouf, I., & Annany, Y. (2018). Special studies in management of construction project risks, risk concept, plan building, risk quantitative and qualitative analysis, risk response strategies. Alexandria engineering journal, 57 (4), 3179-3187.
Klir, G.J. (1997). Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems, 9 (2), 165-175. Available at: https://doi.org/10.1016/S0165-0114(97)00138-3.
Kosheleva O., Cabrera S.D., Gibson G.A., & Koshelev M. (1997). Fast implementations of fuzzy arithmetic operations using fast Fourier transform (FFT). Fuzzy Sets and Systems, 91 (2), 269-277.
Lesage, C. (2001). Discounted cash-flows analysis: An interactive fuzzy arithmetic approach. European Journal of Economic and Social Systems, 15 (2), 49-68.
Liu, H., & Guo, S. (2007). Equality and Identity of Fuzzy Numbers and Fuzzy Arithmetic with Equality Constraints. Proceedings of the 2007 International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2007). 334-339.
Li, Y. (2015). Study on the Personal Credit Risk Evaluation based on Improved Fuzzy AHP Comprehensive Evaluation Method. 6th International Conference on Machinery, Materials, Environment, Biotechnology and Computer, Atlantis Press, 76-79.
Łyczkowska-Hanćkowiak, A. (2020). On Application Oriented Fuzzy Numbers for Imprecise Investment Recommendations. Symmetry, 12 (10), 1672.
Mareš, M. (1997). Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems, 91 (2), 143-153.
Namvar, A., & Naderpour, M. (2018). Handling uncertainty in social lending credit risk prediction with a Choquet fuzzy integral model. 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 1-8.
Pisz, I., Chwastyk, A., & Łapuńka, I. (2019). Assessing the profitability of investment projects using ordered fuzzy numbers. Scientific Journal of Logistics, 15 (3), 377-389.
Purdy, G. (2010). ISO 31000: 2009–setting a new standard for risk management. Risk Analysis: An International Journal, 30 (6), 881-886.
Roy, A.D. (1952). Safety-first and the holding of assets. Econometrics, 20 (3), 431–449.
Saaty, T., & Kearns, K. (1985). Analytical planning: the organization of systems. International series in modern applied mathematics and computer science, 7. Pergamon Press.
Sharpe, W.F. (1966). Mutual fund performance. The Journal of business, 39 (1), 119-138.
Sirbiladze, G., Khutsishvili, I., & Dvalishvili, P. (2010). Decision precising fuzzy technology to evaluate the credit risks of investment projects. 10th International Conference on Intelligent Systems Design and Applications, 103-108.
Stefanini, L., Sorini, L., & Guerra, M.L. (2008). Fuzzy Numbers and Fuzzy Arithmetic. In Pedrycz, W., Skowron, A., & Kreinovich V. (eds). Handbook of Granular Computing, 249-284.
Sugeno, M. (1972). Fuzzy Measure and Fuzzy Integral. Transaction of the Society of Instrument and Control Engineers, 8 (2), 218-226.
Sveshnikov, S., & Bocharnikov, V. (2022). Computational Algorithm and Tools of Fuzzy Arithmetic Based on the Principle of Maximum Entropy. Research Article, preprint. Retrieved from https://doi.org/10.21203/rs.3.rs-1254409/v1.
Takahagi, E. (2000). On identification methods of λ-fuzzy measures using weights and λ. Japan Fuzzy Society Journal, 12 (5), 665-676.
Whelan, J., Msefer, K., & Chung, C.V. (2001). Economic supply & demand. MIT, Cambridge Mass.
Wnuk-Pel, T. (2014). The Practice and Factors Determining the Selection of Capital Budgeting Methods – Evidence from the Field. Procedia - Social and Behavioral Sciences, 156, 612-616.
Wójcicka-Wójtowicz, A., & Piasecki, K. (2021). Application of the Oriented Fuzzy Numbers in Credit Risk Assessment. Mathematics, 9 (5). 535.
Zadeh, L.A. (1975). The Concept of linguistic variable and its applications to approximate reasoning. Information Sciences, 8 (4), 301-357.
The Author wishes to submit the Work to SJM for publication. To enable SJM to publish the Work and to give effect to the parties’ intention set forth herein, they have agreed to cede the first right to publication and republication in the SJM Journal.
Cession
The Author hereby cedes to SJM, who accepts the cession, to the copyright in and to the paper.
The purpose of the cession is to enable SJM to publish the Work, as first publisher world-wide, and for republication in the SJM Journal, and to grant the right to others to publish the Work world-wide, for so long as such copyright subsists;
SJM shall be entitled to edit the work before publication, as it deems fit, subject to the Authors approval
The Author warrants to SJM that:
- the Author is the owner of the copyright in the Work, whether as author or as reassigned from the Author’s employee and that the Author is entitled to cede the copyright to SJM;
- the paper (or any of its part) is not submitted or accepted for publication in any other Journal;
- the Work is an original work created by the Author;
- the Author has not transferred, ceded, or assigned the copyright, or any part thereof, to any third party; or granted any third party a licence or other right to the copyright, which may affect or detract from the rights granted to SJM in terms of this agreement.
The Author hereby indemnifies the SJM as a body and its individual members, to the fullest extent permitted in law, against all or any claims which may arise consequent to the warranties set forth.
No monetary consideration shall be payable by SJM to the Author for the cession, but SJM shall clearly identify the Author as having produced the Work and ensure that due recognition is given to the Author in any publication of the Work.
Should SJM, in its sole discretion, elect not to publish the Work within 1 year after the date of this agreement, the cession shall lapse and be of no further effect. In such event the copyright shall revert to the Author and SJM shall not publish the Work, or any part thereof, without the Author’s prior written consent.