Possible and necessary optimality of solutions in the single machine scheduling problem with fuzzy parameters

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.