Simple Linear Interpolation Explains All Usual Choices in Fuzzy Techniques: Membership Functions, t-Norms, t-Conorms, and Defuzzification

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Jonathan Quijas, The University of Texas at El PasoFollow
Esthela Gallardo, The University of Texas at El PasoFollow
Caio De Sa Lopes, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Shahnaz Shahbazova, Azerbaijan Technical UniversityFollow

Publication Date

3-2015

Comments

Technical Report: UTEP-CS-15-23

Abstract

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.