Linguistic operation time computation in parallel processor scheduling using the 2-tuple fuzzy representation model
Prashant Kumar Gupta, Pranab Kumar Muhuri · 2018
Scheduling is the art of ordering a number of tasks with a fair allocation of resources with the intent of ensuring that these tasks are executed in minimal time. The processors, on which these tasks are executed, can be identical or nonidentical. They may have same or different execution capabilities. In real life situations, these tasks are in need of different types of resources such as network bandwidth, memory and processor speed. These resources are generally attached to the processors and the tasks are executed or assigned to the appropriate processor based on a scheduling algorithm. The scheduling algorithm determines the total execution time required to complete all the tasks all the processors and tries to minimize this total completion time. However, in real life, the values of these scheduling resources are uncertain and therefore they affect the total completion times to varying degrees. As human beings naturally understand and express themselves using words, therefore to incorporate human factors in these scheduling problems, the values of these criteria were specified linguistically in a recent work. The system was designed as a combination of if-then rules and Mamdani inference mechanism was used to determine the crisp value of completion time. Furthermore, the number of if-then rules required to design the system were very large. However, the solution to a problem formulated by the linguistic variables should be in linguistic form. Therefore, in the present work we propose the use of 2-tuple fuzzy linguistic approach to find the solution of parallel processor scheduling involving linguistic data values. The proposed approach is capable of giving linguistic solution using a small sized if-then rule base.