Some Results about the Exponential Of Stochastic Ordering Models

Abstract

This paper explores a new approach for comparing the expectations of stochastic order in fuzzy settings and defines a new expectation ordering that allows for stochastic comparisons of fuzzy random variables. In order to achieve this goal, we first conduct stochastic comparisons of two distinct fuzzy random variables under orders with varying baseline distributions and mixing distributions for the likelihood ratio, hazard rate, mean residual life, and mean inactivity time. The primary benefit of the paper is to comprehend the novel ideas of stochastic comparison of stochastic order built on the exponential order. Proved the preservation properties and theorem by using the fuzzy stochastic orders and created a new definition and applications involving stochastic orders are presented.