Fretting hysteresis loops are multivalued in displacement because loading and unloading branches revisit the same displacement at different tangential forces. This study applies a normalized path coordinate, \( u=\frac{k-1}{N-1} \), to represent displacement and force as the single-valued mappings \( \delta \left(u\right) \)and \( T\left(u\right) \), and compares four first-order Takagi–Sugeno fuzzy models using a 600-point experimental IC25 loop. Ten leakage-c⁠ontrolled 70/30 train–test partition⁠s yielded mean test NRMSEs of 0.00528 for ANFIS–TS, 0.00616 for SC16–TS, 0.00817 for FCM–TS, and 0.01333 for SC9–TS, with no significant difference between ANFIS–T⁠S and SC16–TS after⁠ Holm correcti⁠on (p=0.084)⁠. Physical fidelity and robustness were assessed through dissipated loop energy, peak force, displacement span, closure behavior, cumulative energy evolution, measur⁠ement-nois⁠e sensitivity, residual diagno⁠stics, ru⁠le density, and cycle-origin sensitivity. A same-input RBF–SVR benchmark achieved a lower NRMSE of 0.000838, whereas the fuzzy models retained explicit local rule bases and adjustable complexity. The same nine-rule ANFIS–TS procedure was independently fitted to experimental loops at approximately 1, 14, and 24.5 µm peak-to-peak displacement, demonstrating low-error reconstruction across multiple amplitude conditions without implying zero-shot prediction by a fixed model. Overall, the results establish pat⁠h parameterization as an accurate and int⁠erpretable framework for reconstructing experimental fretting hysteresis rather than as a new friction constitutive law.