A new triangular fuzzy Johnson algorithm

Scheduling consists mainly of allocating resources to jobs over time under necessary constraints. In the past, the processing time for each job was usually assigned or estimated as a fixed value. In many real-world applications, however, job processing times may vary dynamically. McCahon and Lee proposed a fuzzy Johnson algorithm for managing uncertain scheduling. However, some problems exist in their procedure with respect to calculation of the starting time for each job. In this paper, we modify McCahon and Lee's algorithm and propose a new reasonable procedure for eliminating start-time uncertainties. A half-inverse operator is defined and 24 cases are analyzed to verify this procedure. Analytical and experimental results showing the effectiveness of our method are also presented.