This thesis aims to address fuzzy problems in operations research by applying sensitivity analysis based on the properties of ranking functions as an effective mathematical tool to control influential variables. The study relied on a fuzzy membership function and proposed two fuzzy numbers consisting of seven values, based on a single weight function (r) or a two-weight function (r, λ), to enhance the flexibility of membership levels and improve the accuracy of fuzzy models.

The proposed methodology was applied to real data from the General Leather Company for the period (1/12/2022 – 1/3/2023). The results showed that the use of ranking functions in sensitivity analysis provides a structured framework for tracking the relationships among different parameters, reduces uncertainty, and enhances the reliability and accuracy of solutions. Moreover, the comparison with conventional sensitivity analysis demonstrated the superiority of the proposed approach in terms of flexibility and its ability to deal with environments characterized by vagueness and uncertainty.

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