Pythagorean Triangular and Trapezoidal fuzzy assignment problem-Formulations and its Solution

Abstract

The assignment problem is a recognized optimization challenge. Incorporating uncertainties in the problem parameters complicates the efficient resolution of the assignment problem, a frequent occurrence in real-world situations. Pythagorean fuzzy uncertain variables provide a more thorough and balanced depiction of uncertainty by integrating the ideas of uncertainty theory with the advantages of fuzzy logic. Triangular and trapezoidal fuzzy numbers are employed in this paper. Additionally, it employs the branch and bound algorithm to address the Pythagorean ambiguous uncertainty assignment problem. A numerical exemplification is employed to illustrate the algorithm's intricate steps. A novel ranking method is suggested for triangular and trapezoidal fuzzy numbers. The feasibility of integrating Pythagorean fuzzy uncertainty into optimization problems is underscored by the findings.