10.57647/fomj.2026.0701.05

Efficiency Analysis of Insurance Companies under Fuzzy Environment

  1. Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran

Received: 0025-12-18

Revised: 2026-02-12

Accepted: 2026-02-22

Published in Issue 2026-03-30

How to Cite

Gerami, J. (2026). Efficiency Analysis of Insurance Companies under Fuzzy Environment. Fuzzy Optimization and Modeling Journal (FOMJ), 7(1). https://doi.org/10.57647/fomj.2026.0701.05

PDF views: 0

Abstract

Performance evaluation is crucial for the sustainable growth and effective resource allocation of insurance companies. However, the uncertainty and imprecision inherent in operational and financial data limit the applicability of traditional methods. This study proposes a novel fuzzy two-stage data envelopment analysis (DEA) model to assess the efficiency of insurance companies under such conditions. The model employs trapezoidal fuzzy numbers to represent inputs, intermediate measures, and outputs, thereby providing a more robust and realistic efficiency measurement than conventional deterministic DEA. Applied to a dataset of 40 insurance companies, the model yields individual stage efficiencies, overall efficiency scores, and optimal improvement targets for each firm. The key findings reveal that this approach not only identifies significant inefficiencies but also offers actionable strategic insights. Specifically, it enables managers to enhance cost control, optimize policy issuance volumes, accelerate claims settlement, and improve customer satisfaction. These improvements are essential for achieving a sustainable competitive advantage in the highly dynamic insurance market. The study concludes that the fuzzy two-stage DEA model is a valuable tool for both managers and policymakers in making informed decisions for superior resource allocation and performance management in the insurance sector.

References

  1. M. Kamanda & A. B. Sibindi, “Determinants of Financial Performance on Insurance Companies: Empirical Evidence Using Kenyan Data,” Risk and Financial Management, 14(12), 566, 2021.
  2. https://doi.org/10.3390/jrfm14120566
  3. A. Mergoni, A. Emrouznejad, & K. D. Witte, “Fifty Years of Data Envelopment Analysis,” European Journal of Operational Research, 1-25, 2025.
  4. https://doi.org/ 10.1016/j.ejor.2024.12.049
  5. T. Zhao, R. Pei, & J. Pan, “The evolution and determinants of Chinese property insurance companies’ profitability: A DEA-based perspective,” Journal of Management Science and Engineering, 6, 449-466, 2021. https://doi.org/ 10.1016/j.jmse.2021.09.005
  6. 4. A. Charnes, W. W. Cooper, & E. Rhodes, “Measuring the efficiency of decision making units,” European Journal of Operational Research, 2(6), 429-444, 1978.
  7. https://doi.org/10.1016/0377-2217(79)90229-7
  8. R. Färe & S. Grosskopf, “Network DEA,” Socio-economic Planning Science, 34(1), 35–49, 2000. https://doi.org/10.1016/S0038-0121(99)00012-9
  9. C. Kao & S. N. Hwang, “Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan,” European Journal of Operational Research, 185(1), 418–429, 2008. https://doi.org/10.1016/j.ejor.2006.11.041
  10. C. Kao, “Maximum slacks-based measure of efficiency in network data envelopment analysis: A case of garment manufacturing,” Omega, 123, 102989, 2024.
  11. https://doi.org/10.1016/j.omega.2023.102989
  12. S. Ostovan, M. R. Mozaffari, A. Jamshidi, & J. Gerami, “Evaluation of Two-Stage Networks Based on Average Efficiency Using DEA and DEA-R with Fuzzy Data,” International Journal of Fuzzy Systems, 22, 1665–1678, 2020. https://doi.org/10.1007/s40815-020-00896-9.
  13. J. Gerami, M. R. Mozaffari, P. Wanke, & Y. Tan, “Fuzzy cost, revenue efficiency assessment and target setting in fuzzy DEA: a fuzzy directional distance function approach,” Journal of Modelling in Management, 19(1), 240-287, 2024. https://doi.org/10.1108/JM2-05-2022-0121.
  14. J. Gerami, M. R. Mozaffari, P. Wanke, & Y. Tan, “Fully fuzzy DEA: a novel additive slacks-based measure model,” Soft Computing, 2023. https://doi.org/10.1007/s00500-023-08247-8
  15. C. Kao & S. T. Liu, “Efficiencies of two-stage systems with fuzzy data,” Fuzzy Sets and Systems, 176, 20–35, 2011. https://doi.org/10.1016/j.fss.2011.02.017.
  16. A. Emrouznejad, M. Tavana, & A. Hatami-Marbini, “The state of the art in fuzzy data envelopment analysis,” Studies in Fuzziness and Soft Computing, 309, 1–45, 2014.
  17. https://doi.org/10.1007/978-3-319-04711-7_1
  18. N. Arana-Jimenez, M. C. Sanchez-Gill, & S. E. Lozano, “Efficiency assessment and target setting using a fully fuzzy DEA approach,” International Journal of Fuzzy Systems, 22, 1056–1072, 2020.
  19. https://doi.org/10.1007/s40815-020-00821-0A
  20. Hatami-Marbini, M. Tavana, & A. Ebrahimi, “A fuzzy fuzzified data envelopment analysis model,” International Journal of Information and Decision Sciences, 3(3), 252–264, 2011.
  21. https://doi.org/10.1504/IJIDS.2011.041586.
  22. A. Emrouznejad & G. L. Yang, “A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016,” Socio-Economic Planning Sciences, 61, 4-8, 2018.
  23. https://doi.org/10.1016/j.seps.2017.01.008.
  24. W. M. Lu, W. K. Wang, & Q. L. Kweh, “Intellectual capital and performance in the Chinese life insurance industry,” Omega, 42(1), 65-74, 2014. https://doi.org/10.1016/j.omega.2013.03.002.
  25. Y. Chen, W. D. Cook, N. Li, & J. Zhu, “Additive efficiency decomposition in two stage DEA,” European Journal of Operational Research, 96, 1170–1176, 2009. https://doi.org/10.1016/j.ejor.2008.05.011.
  26. K. A. Chrysafis, G. C. Papadopoulou, & I. N. Theotokas, “Measuring financial performance through operating business efficiency in the global cruise industry: A fuzzy benchmarking study on the ‘big three’,” Tourism Management, 100, 104830, 2024. https://doi.org/10.1016/j.tourman.2023.104830
  27. E. Soltanzadeh & H. Omrani, “Dynamic network data envelopment analysis model with fuzzy inputs and outputs: An application for Iranian Airlines,” Applied Soft Computing, 63, 268–288, 2021. https://doi.org/10.1016/j.asoc.2021.107648
  28. X. Zhou, W. Pedrycz, Y. Kuang, & Z. Zhang, “Type-2 fuzzy multiobjective DEA model: An application to sustainable supplier evaluation,” Applied Soft Computing, 46, 424–440, 2016.
  29. https://doi.org/10.1016/j.asoc.2016.04.038. Y. Zhou, Ch. Yan, & X. Wang, “Higher-order moment fuzzy portfolio selection model based on neural networks: Integrating behavioral finance and complex system analysis,” Chaos, Solitons & Fractals, 201, 117195, 2025. https://doi.org/10.1016/j.chaos.2025.117195
  30. M. R. Mozaffari, S. Mohammadi, P. F. Wanke, & H. L. Correa, “Towards greener petrochemical production: Two-stage network data envelopment analysis in a fully fuzzy environment in the presence of undesirable outputs,” Expert Systems With Applications, 164, 113903, 2021. https://doi.org/10.1016/j.eswa.2020.113903
  31. B. S. Mahapatra, D. Ghosh, D. Pamucar, & G. S. Mahapatra, “Dynamic group decision-making for enterprise resource planning selection using two-tuples Pythagorean fuzzy MOORA approach,” Expert Systems with Applications, 263, 125675, 2025. https://doi.org/10.1016/j.eswa.2024.125675
  32. P. Peykani, E. Mohammadi, & A. Emrouznejad, “An Adjustable Fuzzy Chance-Constrained Network DEA Approach with Application to Ranking Investment Firms,” Expert Systems with Applications, 166, 113938, 2021. https://doi.org/10.1016/j.eswa.2020.113938
  33. P. Peykani, M. Sargolzaei, F. Hamidzadeh, F. S. Seyed Esmaeili, & A. Takaloo, “Possibilistic Network DEA Approach for Performance Evaluation of Two-Stage Decision Making Units Under Uncertainty,” Analytical Decision Making and Data Envelopment Analysis: Advances and Challenges, 59-79, 2024. https://doi.org/10.1007/978-981-97-6972-8_3
  34. P. Peykani, A. Mahmoodirad, & A. Amirteimoori, “A novel adjustable intuitionistic fuzzy framework for two-stage data envelopment analysis: An application in the banking sector,” Information Sciences, 718, 122372, 2025. https://doi.org/10.1016/j.ins.2025.122372
  35. S. Saati, A. Memariani, & G. R. Jahanshahloo, “Efficiency analysis and ranking of DMUs with fuzzy data,” Fuzzy Optimization and Decision Making, 1, 255-267, 2002. https://doi.org/10.1023/A:1019648512614
  36. P. Guo & H. Tanaka, “Fuzzy DEA: a perceptual evaluation method,” Fuzzy Sets and Systems, 119(1), 149-160, 2001. https://doi.org/10.1016/S0165-0114(99)00106-2
  37. S. Lertworasirikul, S. C. Fang, J. A. Joines, & H. L. W. Nuttle, “Fuzzy data envelopment analysis (DEA): a possibility approach,” Fuzzy Sets and Systems, 139(2), 379–394, 2003. https://doi.org/10.1016/S0165-0114(02)00484-0
  38. M. Tavana, R. Khanjani Shiraz, A. Hatami-Marbini, P. J. Agrell, & K. Paryab, “Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC),” Expert System with Applications, 39, 12247-12259, 2012. https://doi.org/10.1016/j.eswa.2012.04.049
  39. S. Mehdizadeh, A. Amirteimoori, V. Charles, M. H. Behzadi, & S. Kordrostami, “Measuring the Efficiency of Two-Stage Network Processes: A Satisficing DEA Approach,” Journal of the Operational Research Society, 72(2), 354-366, 2021. https://doi.org/10.1080/01605682.2019.1654933
  40. H. Pourbabagol, M. Amiri, M. T. Taghavifard, & P. Hanafizadeh, “A New Fuzzy DEA Network Based on Possibility and Necessity Measures for Agile Supply Chain Performance Evaluation: A Case Study,” Expert Systems with Applications, 2023. https://doi.org/10.1016/j.eswa.2023.119552
  41. A. Amirteimoori, T. Allahviranloo, M. Zadmirzaei, & F. Hasanzadeh, “On the environmental performance analysis: A combined fuzzy data envelopment analysis and artificial intelligence algorithms,” Expert Systems with Applications, 224, 119953, 2023. https://doi.org/10.1016/j.eswa.2023.119953
  42. A. Amirteimoori, T. Allahviranloo, & S. M. F. Mousavi, “Returns-to-scale and scale economies of two-stage production processes using a fully fuzzy range-adjusted measure model with strong complementary slackness conditions,” Expert Systems with Applications, 262, 125606, 2024. https://doi.org/10.1016/j.eswa.2024.125606
  43. F. Hamidzadeh, M. S. Pishvaee, & N. Zarrinpoor, “A Novel Two-Stage Network Data Envelopment Analysis Model for Kidney Allocation Problem under Medical and Logistical Uncertainty: A Real Case Study,” Management Science, 27, 555–579, 2024. https://doi.org/10.1007/s10729-024-09683-6
  44. S. E. Shojaie, S. J. Sadjadi, & R. Tavakkoli-Moghaddam, “Malmquist Productivity Index under Network Structure and Negative Data: An Application to Banking Industry,” Journal of System Management, 10(3), 107-118, 2024. https://sanad.iau.ir/Journal/sjsm/Article/918428
  45. M. Rezakhanlou & S. Mirzapour, “A dual-channel multi-objective green supply chain network design considering pricing and transportation mode choice under fuzzy uncertainty,” Environment, Development and Sustainability, (27), 10341–10372, 2025. https://doi.org/10.1007/s10668-023-04312-8
  46. A. Garrido, L. E. Cárdenas-Barrón, O. Y. Buitrago, & L. Álvarez-Pomar, “A Multi-Echelon globalized Agro-Industrial supply chain under conditions of Uncertainty: A Two-Stage Fuzzy-Possibilistic Mixed-Integer linear programming Model,” Expert Systems with Applications, 270, 126569, 2025. https://doi.org/10.1016/j.eswa.2025.126569
  47. L. Huang & L. Chen, “Fuzzy random multi-objective optimization using a novel mixed fuzzy random inverse DEA model in input-output production,” Journal of Computational and Applied Mathematics, 470, 116717, 2025. https://doi.org/10.1016/j.cam.2025.116717
  48. M. A. Sahil, A. Tiwari, & Q. M. D. Lohani, “Two-stage type-2 fuzzy parabolic double frontier data envelopment analysis,” Engineering Applications of Artificial Intelligence, 144, 110154, 2025.
  49. https://doi.org/10.1016/j.engappai.2025.110154
  50. Sh. Yan, Y. Xu, J. Liu, & F. G. Cabrerizo, “A fuzzy group decision-making method integrating cooperative game theory and quantum cognition for dynamic trust network,” Expert Systems with Applications, 307, 131045, 2026. https://doi.org/10.1016/j.eswa.2025.131045
  51. M. M. Jaloudi, “The efficiency of Jordan insurance companies and its determinants using DEA, slacks, and logit models,” Journal of Asian Business and Economic Studies, 26(1), 153-166, 2019.
  52. https://doi.org/10.1108/JABES-06-2018-0022
  53. O. Koc, F. Baser, & A. S. Selcuk-Kestel, “Clustering based fuzzy classification with a noise cluster in detecting fraud in insurance,” Applied Soft Computing, 167, 112430, 2024.
  54. https://doi.org/10.1016/j.asoc.2024.112430
  55. K. Polyakov & M. Polyakova, “Determinants of the quality of financial management of insurance companies,” Procedia Computer Science, 242, 1125-1132, 2024.
  56. https://doi.org/10.1016/j.procs.2024.08.185
  57. K. Smętek, A. Strzelecka, & D. Zawadzka, “Examples of the application of the Dynamic Financial Analysis (DFA) method to assess the financial situation and solvency of insurance companies,” Procedia Computer Science, 246, 4787-4795, 2024. https://doi.org/10.1016/j.procs.2024.09.344
  58. P. Liu, H. Sun, & H. Xu, “Performance evaluation of Chinese and foreign property insurance companies considering negative data: Based on the dynamic two-stage IBP-SBM model,” Socio-Economic Planning Sciences, 98, 102169, 2025. https://doi.org/10.1016/j.seps.2025.102169
  59. M. Özçalici, D. Pamucar, H. E. Gurler, N. G. Karyağdi, & A. Kaya, “A robust hybrid MCDM framework with emphasis on decision stability intervals: Performance evaluation of global insurance brokers using fuzzy LBWA and modified ARTASI,” Applied Soft Computing, 190, 114557, 2026. https://doi.org/10.1016/j.asoc.2026.114557.
  60. S. J. Ho & H. H. Hsu, “The effect of microinsurance on the insurance market: evidence from Taiwan,” The Geneva Papers on Risk and Insurance - Issues and Practice, 46(1), 130-145, 2021.
  61. https://doi.org/10.1057/s41288-020-00175-6
  62. J. Jia-Ying, L. J. Zhou, W. Shen, X. Li, J. Huizhen, & P. Wentsao, “Performance evaluation and analysis of Chinese insurance companies under uncertain financial markets,” Heliyon, 9(11), e21487, 2023. https://doi.org/10.1016/j.heliyon.2023.e21487
  63. F. S. Seyed Esmaeili & E. Mohammadi, “Z-Number Network Data Envelopment Analysis Approach: A Case Study on the Iranian Insurance Industry,” Plos One, 19(7), e0306876, 2024. https://doi.org/10.1371/journal.pone.0306876
  64. S. H. Nasseri & M. A. Khatir, “Fuzzy Stochastic Undesirable Two-Stage Data Envelopment Analysis Models with Application to Banking Industry,” Journal of Intelligent & Fuzzy Systems, 37(5), 7047-7057, 2019. https://doi.org/10.3233/JIFS-181684
  65. A. Nosrat, M. Sanei, A. Payan, F. Hosseinzadeh Lotfi, & S. Razavyan, “Using Credibility Theory to Evaluate the Fuzzy Two-Stage DEA; Sensitivity and Stability Analysis,” Journal of Intelligent & Fuzzy Systems, 37(4), 5777-5796, 2019. https://doi.org/10.3233/JIFS-181519
  66. K. Ohene-Asare, J. K. A. Asare, & C. Turkson, “Dynamic cost productivity and economies of scale of Ghanaian insurers,” The Geneva Papers on Risk and Insurance - Issues and Practice, 44, 148–177, 2019. https://doi.org/10.1057/s41288-018-0111-6
  67. H. J. Zimmermann, “Introduction to Fuzzy Sets,” In: Fuzzy Set Theory—and Its Applications, Springer, Dordrecht, 2001. https://doi.org/10.1007/978-94-010-0646-0-1
  68. S. Lozano, “Process efficiency of two-stage systems with fuzzy data,” Fuzzy Sets and Systems, 243, 36–49, 2014. https://doi.org/10.1016/j.fss.2013.05.012