Interactive Fuzzy Programming for Random Fuzzy Two-Level Integer Programming Problems through Fractile Criteria with Possibility

This paper considers two-level integer programming problems involving random fuzzy variables with cooperative behavior of the decision makers. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile criteria to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level integer programming problems are reduced to deterministic ones. Through the introduction of genetic algorithms with double strings for nonlinear integer programming problems, interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.

Seismic reliability analysis of large electric power systems

Based on the De.Morgan laws and Boolean simplification, a recursive decomposition method is introduced in this paper to identify the main exclusive safe paths and failed paths of a network. The reliability or the reliability bound of a network can be conveniently expressed as the summation of the joint probabilities of these paths. Under the multivariate normal distribution assumption, a conditioned reliability index method is developed to evaluate joint probabilities of various exclusive safe paths and failed paths, and, finally, the seismic reliability or the reliability bound of an electric power system. Examples given in the paper show that the method is very simple and provides accurate results in the seismic reliability analysis.