The objective of this paper is to deal with the analytical properties of credibility critical value functions. Based on the continuity of credibility functions, several sufficient and necessary conditions for some properties of the credibility critical value functions are established. The results obtained in this paper can be used to fuzzy optimization problems as we design algorithms to compute the critical values of objective functions.

By dealing with interarrival times as exponentially distributed fuzzy random variables, a fuzzy random homogeneous Poisson process and a fuzzy random compound Poisson process are respectively defined. Several theorems on the two processes are provided, respectively.

There are two types of critical values for birandom variable: the optimistic and pessimistic values. In this paper, some theoretical aspects of optimistic and pessimistic values of birandom variable are investigated. Based on the results, some properties of birandom chance-constrained programming models can be further discussed.

In this paper, a fuzzy inventory problem with multiple commodities is casted into a dynamic pro- gramming model with continuous state space and decision space. In order to solve the dynamic programming model, genetic algorithms are used to get samples of the optimal cost functions, and then neural networks are trained to approximate the optimal cost function on a randomly generated sample set, which may bypass “the curse of dimensionality”. A hybrid intelligent algorithm is thus produced to get the optimal cost functions functions that represented by neural networks. Lastly, a numerical example is given for illustrating purpose

This paper introduces a new optimization problem for a TV station to accept and schedule adver- tisements. The TV station has its advertising slots with audience ratings, and the advertisers purchase audience ratings. The objective of the TV station is to maximize the total revenue by simultaneously accepting some of the advertisements and finding a feasible schedule for them. An integer programming model is formulated and three heuristic algorithms are proposed. The numerical experiments show that these heuristics are effective.

Fuzzy random variable is defined as a measurable function from the probability space to the set of fuzzy numbers.In this paper,the concept of uniform convergence of fuzzy random sequence is presented.Additionally,some mathematical properties of convergent fuzzy random sequence are also obtained.