Stochastic programming with fuzzy linear partial informaton on probability distribution

This paper deals with stochastic programming problems where the probability distribution is not explicitly known. We suppose that the probability distribution is defined by crisp or fuzzy inequalities on the probability of the different states of nature. We formulate the problem and present a solution strategy that uses the α-cut technique in order to transform our problem into a stochastic program with linear partial information on probability distribution (SPI). The obtained SPI problem is then solved using two approaches, namely, a chance constrained approach and a recourse approach. For the recourse approach, a modified L-shaped algorithm is designed and illustrated by an example.