A Numerical-Integration-Based Simulation Algorithm for Expected Values of Strictly Monotone Functions of Ordinary Fuzzy Variables

Fuzzy simulation is used to approximate the expected values of functions of fuzzy variables, which plays an important role in the solution algorithms of fuzzy optimization problems. The traditional discretization-based simulation algorithms fail to return a satisfactory approximation within an acceptable computation time, which hinders the applications of fuzzy optimization methods in large-size or even middle-size problems. In this paper, we first prove some equivalent formulas for the expected values of strictly monotone functions of ordinary fuzzy variables. Then, we propose a new fuzzy simulation algorithm based on the numerical integration technique. Finally, we present some numerical examples to make comparisons between the traditional approach and our approach. The results show that our approach has higher performances on the reliability, stability, and computation time.