Simple linear interpolation explains all usual choices in fuzzy techniques: Membership functions, t-norms, t-conorms, and defuzzification
Владик Крейнович, Jonathan Quijas, Esthela Gallardo, Caio De Sa Lopes, Olga M. Kosheleva, Shahnaz N. Shahbazova · 2015
Most applications of fuzzy techniques use piece-wise linear (triangular or trapezoid) membership functions, min or product t-norms, max or algebraic sum t-conorms, and centroid defuzzification. Similarly, most applications of interval-valued fuzzy techniques use piecewise-linear lower and upper membership functions. In this paper, we show that all these choices can be explained as applications of simple linear interpolation.