IFSJSP: A novel methodology for the Job-Shop Scheduling Problem based on intuitionistic fuzzy sets

The Job-Shop Scheduling Problem (JSP) is an important concern in advanced manufacturing systems. In real applications, uncertainties exist practically everywhere in the JSP, ranging from engineering design to product manufacturing, product operating conditions and maintenance. A variety of approaches have been proposed to handle the uncertain information. Among them, the Intuitionistic Fuzzy Sets (IFS) is a novel tool with the ability to handle vague information and is widely used in many fields. This paper develops a method to address the JSP under an uncertain environment based on IFSs. Another contribution of this paper is to put forward a generalised (or extended) IFS to process the additive operation and to compare the operation between two IFSs. The methodology is illustrated using a three-step procedure. First, a transformation is constructed to convert the uncertain information in the JSP into the corresponding IFS. Secondly, a novel addition operation between two IFSs is proposed that is suitable for the JSP. Then a novel comparison operation on two IFSs is presented. Finally, a procedure is constructed using the chromosome of an operation-based representation and a genetic algorithm. Two examples are used to demonstrate the efficiency of the proposed method. In addition, a comparison between the results of the proposed IFSJSP and other existing approaches demonstrates that IFSJSP significantly outperforms other existing methods.