Abstract
Background The conventional Assignment Problem (AP) may no longer be sufficient to handle real-world problems as they get more multifaceted and incorporate numerous, frequently conflicting objectives. In response, the Bi-Objective Assignment Problem (BOAP) provides an extended optimization framework that enables the simultaneous consideration of two competing objectives to obtain more effective solutions. Methods This research paper proposes a combination of two innovative approaches to solve BOAPs based on interval data. First, the interval-based BOAP is converted into a fuzzy AP using the Trisectional approach, and second, a proposed ranking technique based on the concept of the in-centre is applied to defuzzify it into a crisp number. A proposed algorithm is used to solve bi-objective optimization problems. The goal of this study is to find the efficient and non-efficient solutions for the BOAP. We also want to find a compromise solution for the BOAP using the proposed trisectional fuzzy trapezoidal approach. Results This approach is better for the decision maker (DM) who makes decisions, and it works better than other approaches. This is supported by numerical illustrations and its solutions are presented in a graph. A comparison with existing approaches demonstrates the effectiveness and significance of the proposed method for APs involving interval data. Furthermore, a sensitivity analysis (SA) is performed to examine the influence of key parameters on the performance and outcomes of the proposed model. Conclusions For the specified AP, the proposed approach effectively finds the complete set of efficient solution (ES) as well as the best compromise solution. Additionally, a comparison with current approaches shows that the proposed methodology is superior in terms of decision-making flexibility and solution quality. The decision-maker (DM) has more freedom to choose the best option given realistic financial and operational restrictions when there are several effective options available.