What Is the Uncertainty of the Result of Data Processing: Fuzzy Analogue of the Central Limit Theorem

Authors

Julio C. Urenda, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Shahnaz Shahbazova, Azerbaijan Technical UniversityFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-1-2021

Comments

Technical Report: UTEP-CS-21-67

Abstract

It is known that, due to the Central Limit Theorem, the probability distribution of the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a distribution from a somewhat more general class known as infinitely divisible. We show that a similar result holds in the fuzzy case: namely, the membership function describing the uncertainty of the result of data processing is, in general, close to Gaussian -- or to a membership function from an explicitly described more general class.