A Novel Approach to Sequencing Problems Using Type-2 Pentagonal Fuzzy Numbers and Centroid Defuzzification: Sequencing Problems Using Type-2 Pentagonal Fuzzy Numbers

Abstract

Sequencing problems play a crucial role in determining the optimal order for executing a set of critical tasks, with the primary objective of minimizing the total time required to complete all the tasks. Traditionally, in classical job sequencing problems, it is assumed that the processing times for each task are known with certainty and are treated as fixed values. However, in real-world scenarios, it is often observed that the actual processing times are not precisely known in advance and tend to be uncertain or variable due to various unforeseen factors.
To address this uncertainty, fuzzy job sequencing models are employed, where the processing times are represented using fuzzy numbers to better capture the inherent vagueness and imprecision. In this study, a solution methodology is proposed for tackling fuzzy job sequencing problems, where Type-2 fuzzy numbers are specifically utilized to model the uncertain processing times more accurately.
A suitable defuzzification measure is applied to convert the fuzzy processing times into crisp (non-fuzzy) values, effectively transforming the original fuzzy sequencing problem into a standard, deterministic sequencing problem. Once defuzzified, the resulting crisp problem is solved using conventional sequencing algorithms to determine the optimal task sequence and the corresponding minimum completion time. This approach provides a more realistic and practical solution framework for job sequencing problems encountered in environments characterized by uncertainty and imprecision.
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