The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is widely recognized and proven as an effective approach for ranking alternatives within a multi-attribute group decision-making (MAGDM) scenario. In such contexts, the selection of appropriate distance metrics holds paramount importance. Interval-valued Fermatean fuzzy numbers are renowned for their effectiveness in encapsulating fuzzy information better than intuitionistic and Fermatean fuzzy numbers within MAGDM problems. Despite the availability of distance metrics for interval-valued Fermatean fuzzy numbers, certain scenarios exist where these metrics are inadequate in discerning the differences between two such fuzzy numbers, consequently leading to conflicting results. Addressing this issue is the primary objective of the present research endeavour. First, the triangular divergence measure has been utilized to propose a modified distance metric for interval-valued Fermatean fuzzy sets and its properties are investigated. Through a comparative analysis with existing metrics, the superiority of the proposed distance measure is demonstrated. Subsequently, the traditional TOPSIS method undergoes modification by incorporating the newly proposed triangular divergence-based distance metric in the interval-valued Fermatean fuzzy environment. To illustrate the proposed method’s practicality, a numerical example is presented. The efficacy of the proposed modified TOPSIS method is evaluated through comparison with existing approaches within the context of interval-valued Fermatean fuzzy sets. The results of the comparative analysis illustrate that the proposed method effectively distinguishes fine differences in interval-valued Fermatean fuzzy sets. The results of this study show that the proposed triangular divergence-based distance metric not only modifies the existing TOPSIS approach but also improves its overall effectiveness and precision across various MAGDM techniques.