Why Triangular and Trapezoid Membership Functions: A Simple Explanation

  • Vladik KreinovichEmail author
  • Olga Kosheleva
  • Shahnaz N. Shahbazova
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 391)


In principle, in applications of fuzzy techniques, we can have different complex membership functions. In many practical applications, however, it turns out that to get a good quality result – e.g., a good quality control – it is sufficient to consider simple triangular and trapezoid membership functions. There exist explanations for this empirical phenomenon, but the existing explanations are rather mathematically sophisticated and are, thus, not very intuitively clear. In this paper, we provide a simple – and thus, more intuitive – explanation for the ubiquity of triangular and trapezoid membership functions.


Fuzzy logic Triangular membership function Trapezoid membership function 



This work was supported in part by the National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence). The authors are thankful to all the participants of the 7th World Conference on Soft Computing (Baku, Azerbaijan, May 29–31, 2018) for valuable discussions.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vladik Kreinovich
    • 1
    Email author
  • Olga Kosheleva
    • 1
  • Shahnaz N. Shahbazova
    • 2
  1. 1.University of Texas at El PasoEl PasoUSA
  2. 2.Azerbaijan Technical UniversityBakuAzerbaijan

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