programming with
fuzzy probability distribution** **

**Abstract:** 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
alpha-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
than 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.

**Keywords**: stochastic programming, fuzzy sets, alpha-cut technique, chance
constrained approach, recourse approach, L-shaped method