New fuzzy simulation-based algorithms for the credibility of fuzzy events

Accurate and computationally efficient methodologies for developing fuzzy simulation-based algorithms for the calculation of the credibility of a fuzzy event not only continue to constitute great challenges for researchers, but their importance to practitioners for solving real-world applications is steadily increasing ever since. In this regard, we develop and test two simulation-based algorithms using the uniform discretization method and the bisection approach based upon the monotonicity of shape functions of regular fuzzy numbers, accordingly. A comparison analysis is conducted which verifies higher levels of accuracy and efficiency for them when the standard stochastic discretization algorithm is used as a benchmark. In addition, we propose two simulation-based algorithms as their extension for the calculation of the credibility of a joint fuzzy event. Their formulation is a result of two new theorems which provide distinct ways to connect the credibility of a joint fuzzy event with its components. A series of numerical experiments are considered for demonstrating clearly the accuracy and computational efficiency of the treatment.