Abstract
The single machine scheduling problem with parameters given in the form of fuzzy numbers is considered. It is assumed that the optimal schedule in such a problem cannot be determined precisely (since the parameters of the problem are not known a priori). In this paper the concepts of possible and necessary optimality of a given schedule are introduced. The degrees of possible and necessary optimality measure the possibility and the necessity of the event that a given schedule will be optimal. In this paper, it is shown how to calculate the degrees of possible and necessary optimality of a given schedule in one of the special cases of the single machine scheduling problems.
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