This research provides a new distance measure, named logarithmic lp distance, for interval-valued Fermatean fuzzy sets (IVFFSs), which is utilized in a hybrid model of VIKOR-TOPSIS in order to solve the problem of multiple criteria decision-making regarding battery swap station location selection in new energy vehicle systems. This distance measure considers the membership and non-membership values cubed using logarithmic conversion, where the value of parameter p provides sensitivity adjustment capability. The measure strictly satisfies the properties of a conventional metric distance measure of non-negative values, symmetry, finiteness, and the triangular rule. Combining the closeness concept typical of TOPSIS and the regret approach associated with VIKOR leads to the application of the developed combined model to assess five station locations using six performance indices, two of which are related to NEV conditions, including NEV ownership coverage and charging facilities complementarity. It has been demonstrated that the optimal location for the station construction is the highway service area junction (F = 1.0000), regardless of different parameters and weights used. Cross-method comparisons further reveal that the proposed measure achieves finer discrimination among closely evaluated alternatives than its Euclidean and Hamming counterparts.
