Minimisation of the expected weighted number of jobs being late with fuzzy processing time in a one machine system

One machine scheduling problem with fuzzy processing times and a penalty for each job being late (the penalty is independent of the magnitude of the lateness) is considered. The optimal sequence is defined as one minimizing the expected value of the total penalty (the expected weighted number of jobs being late). Two special cases are discussed in which the problem can be reduced to well-known and easy to solve optimization problems.