Measure of quality and certainty approximation of functional inequalities

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 $ diag(X, Y, X\ast 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.

Keywords

• fuzzy sets
• probability distribution function
• z-numbers
• functional inequality
• jordan-von neumann functional equation
• gauss hypergeometric function
• mittag leffler function