A Two-Stage Interval Type-2 Fuzzy Approach for Contract Renewal Risk Assessment in Non-Life Insurance Using BWM and Pareto Analysis

Abstract

The accurate assessment of contract renewal risk at the individual policyholder level represents a critical component of risk management in non-life insurance and is essential for ensuring long-term business sustainability. In this study, a two-stage interval type-2 fuzzy decision-making framework was proposed to evaluate and classify policyholder renewal risk. The approach began with the identification of key risk factors (RFs) that exert the most significant influence on renewal outcomes and overall business risk. The relative importance of these RFs was expressed through predefined linguistic terms, which were systematically mapped to interval type-2 triangular fuzzy numbers (IT2TFNs). The Fuzzy Best-Worst Method (FBWM) was applied to derive the optimal weight vector of RFs. Subsequently, the values of the identified RFs were quantified based on available operational and historical insurance data. Using type-2 fuzzy algebra, a weighted normalized decision matrix was constructed. In the second stage, a novel Pareto analysis extended with interval type-2 fuzzy numbers (IT2FNs) was introduced to classify policyholders according to their associated renewal risk levels. This integration enabled the simultaneous consideration of both factor weights and their fuzzy performance values, ensuring that high-risk policyholders are effectively distinguished from lower-risk groups. The proposed framework was validated through a real-world case study in the non-life insurance sector. By integrating the strengths of FBWM and fuzzy Pareto analysis, the framework provides an original and rigorous methodology for risk assessment in non-life insurance, contributing to both academic research and practical applications in the domain of sustainable insurance management.