Optimal fuzzy counterparts of scheduling rules

The optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using probability theory is examined formally. Fuzzy scheduling techniques proposed in the literature either fuzzify directly the existing scheduling rules, or solve mathematical programming problems to determine the optimal schedules. In the former method, the fuzzy optimality for the optimal scheduling rules is usually not justified but still assumed. In this paper, the necessary conditions for fuzzy optimality are defined, and fuzzy counterparts of some of the well-known scheduling rules such as shortest processing time and earliest due date are developed.