Title: On multi-objective extensions of the classical assignment model with fuzzy parameters and fuzzy goals

Authors: Lanndon Ocampo; Enrico Enriquez; Carmelita Loquias; Reuella J Bacalso; Grace Estrada

Addresses: Department of Computer, Information Sciences and Mathematics, University of San Carlos, Cebu City, 6000, Philippines; Center for Applied Mathematics and Operations Research, Cebu Technological University, M.J. Cuenco Ave., Corner R. Palma St., Cebu City, 6000, Philippines ' Department of Computer, Information Sciences and Mathematics, University of San Carlos, Cebu City, 6000, Philippines ' Department of Computer, Information Sciences and Mathematics, University of San Carlos, Cebu City, 6000, Philippines ' Department of Computer, Information Sciences and Mathematics, University of San Carlos, Cebu City, 6000, Philippines ' Department of Computer, Information Sciences and Mathematics, University of San Carlos, Cebu City, 6000, Philippines

Abstract: This study advances the limitations of current fuzzy multi-objective assignment models by exploring some formulations with fuzzy parameters and fuzzy goals. The first formulation expresses the coefficients of the objective functions and constraints as fuzzy sets. Two crucial fuzzy transformations were adopted, along with the computational process of the epsilon-constrained multi-objective optimisation. On the other hand, the second formulation assumes the fuzzy coefficients of objective functions and constraints and extends such fuzziness by introducing fuzzy constraints. Lastly, the coefficients of the objective functions and the constraints are expressed as crisp sets while allowing permissible constraint violations. The symmetric fuzzy linear programming solution concepts in the domain literature were adopted as part of the computational process in arriving at a model solution. Actual case examples aided these formulations to gain insights into their computational complexity, efficiency, scalability, and flexibility.

Keywords: assignment; multi-objective optimisation; fuzzy optimisation.

DOI: 10.1504/IJMOR.2022.123118

International Journal of Mathematics in Operational Research, 2022 Vol.22 No.1, pp.93 - 126

Received: 05 Jan 2021
Accepted: 07 Apr 2021
Published online: 30 May 2022 *

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