Solving multi-objective linear fractional decentralized bi-level decision-making problems through compensatory intuitionistic fuzzy mathematical method

Abstract

This study has focused on developing a new method for solving the multi-objective linear fractional decentralized bi-level decision-making (MOLF-DBLDM) problem in an intuitionistic fuzzy decision environment. The main motivation behind this study is to determine a solution approach algorithm that is effective and simple to apply while taking actual decision-making circumstances into account. Real-world decision-making situations involve a bi-level of several decision-makers who use various decision-making processes such as agree, not certain, and disagree. By considering such real-world conditions here, all uncertain coefficients of objectives, constraint functions, and resources are portrayed as trapezoidal intuitionistic fuzzy numbers, and their crisp form is obtained through the (α,β)-cut (confidence level) concept. In the suggested method, we have transformed the crisp (α,β)-MOLF-DBLDM problem into a single objective linear decentralized bi-level decision-making (SOL-DBLDM) model using a modified linearized approach. Additionally, the upper level specified a tolerance region for its decision variables to regulate the lower levels in order to prevent decision lock. Then, the SOL-DBLDM problem is expressed as a single-level model using a new scalar function of membership and non-membership degree for each objective function at all decision-makers and upper level decision control variables. The key advantage of this method over others is that it produces an alternate, preferable compromise solution to the problem of imprecise hierarchical-level optimization. Finally, comparisons to the current methodology and appropriate numerical examples are used to demonstrate the superiority and effectiveness of the suggested method.