SoftTri: Smooth Triangular Membership Functions for Adaptive Fuzzy Inference Systems
Triangular membership functions (MFs) are widely used in fuzzy systems because of their interpretability, low parameterization complexity, and strong locality properties. However, their inherent nondifferentiability at knot points limits the effectiveness of gradient-based optimization in adaptive neuro-fuzzy architectures, often necessitating subgradient approximations or heuristic smoothing techniques. In this paper, we propose \emph{SoftTri}, a differentiable triangular membership function constructed using a smooth soft-hinge mechanism inspired by Swish-type activations. The proposed formulation preserves the geometric structure and localized behavior of classical triangular MFs while...
| Authors | Babak Sarani, Rahman Ardakanian, Ali Mousavi |
|---|---|
| Primary category | cs.LG |
| Published | 26 July 2026 |
| Last updated at source | 26 July 2026 |
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