@article{Eidinejad2024, 
author = {Zahra Eidinejad and Reza Saadati and Donal O'Regan and Fehaid Salem Alshammari},
title = {Measure of quality and certainty approximation of functional inequalities},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {2022-2031},
keywords = {fuzzy sets, probability distribution function, Z-numbers, functional inequality, Jordan-von Neumann functional equation, Gauss hypergeometric function, Mittag Leffler function},
url = {https://www.sciopen.com/article/10.3934/math.2024100},
doi = {10.3934/math.2024100},
abstract = {To make a decision to select a suitable approximation for the solution of a functional inequality, we need reliable information. Two useful information ideas are quality and certainty, and the measure of quality and certainty approximation of the solution of a functional inequality helps us to find the optimum approximation. To measure quality and certainty, we used the idea of the Z-number (Z-N) and we introduced the generalized Z-N (GZ-N) as a diagonal matrix of the form    d  i  a  g  (  X  ,  Y  ,  X  ∗  Y  ), where    X is a fuzzy set time-stamped,    Y is the probability distribution function and the third part is the fuzzy-random trace of the first and the second subjects. This kind of diagonal matrix allowed us to define a new model of control functions to stabilize our problem. Using stability analysis, we obtained the most suitable approximation for functional inequalities.}
}