Defuzzification of intuitionistic fuzzy thermal diffusivity in heat equation: Comparative analysis of methods

This study aims to enhance the modeling of heat transfer under uncertainty by representing thermal diffusivity as an intuitionistic triangular fuzzy number (ITFN) and comparing various defuzzification methods. The methodology involves fuzzifying the nominal thermal diffusivity of copper (approximately 1.11×10⁻⁴ m²/s) into an ITFN, followed by the application of three defuzzification techniques—weighted average, score function-based, and centroid methods—to derive crisp values. Numerical simulations of the heat equation were conducted using these DE fuzzified values to assess their impact on temperature distribution predictions. Findings indicate that the weighted average and centroid methods yield nearly identical values (1.113×10⁻⁴ m²/s), whereas the score function-based method produces a slightly higher value of 1.158×10⁻⁴ m²/s. Although differences in predicted temperature profiles are minimal for copper, the study highlights that for materials with greater variability, the choice of defuzzification method may significantly influence simulation outcomes. These results suggest that employing ITFNs in heat transfer modeling provides a robust framework for capturing material uncertainties, thereby improving the reliability of engineering analyses in uncertainty-sensitive applications.