Fuzzy Multi-Choice Goal Programming and Artificial Bee Colony Algorithm for Triangular and Trapezoidal Membership Functions

Multi-choice goal programming (MCGP) has been widely used to find satisfying solutions for multiple criteria/objective decision problems in which the target value of “the more, the better,” or “the less, the better” can easily be obtained. This paper proposes two new models for representing the triangular and trapezoidal membership functions, which improve the efficacy of fuzzy MCGP (FMCGP). Two real-world applications are provided in this study to demonstrate the usefulness of the proposed models. Furthermore, the same problems are resolved by using the proposed nature-inspired optimization method (NIOM) to find the differences between them. While the artificial bee colony (ABC) algorithm is a well-known NIOM technique, studies have shown that it has an excellent performance with high-quality solutions. Thus, this study initially uses the ABC algorithm to find the differences between MCGP and ABC. Finally, some insightful information is obtained from the comparison to contribute to the NIOM and MCGP fields and their respective applications.