A Generalized Framework for Multivariate Neutrosophic Random Vectors and Their Statistical Properties

Abstract

This paper discusses an aspect of the generalized neutrosophic concept of neutrosophic random variables, specifically for modeling uncertainty and indeterminacy in complex random systems. The study presents a precise and extended formulation of multivariable neutrosophic random vector constructs and their common structures, thereby providing a more comprehensive approach by discussing classical probability theories and reformulating them according to neutrosophic logic. Furthermore, the properties of multivariable common neutrosophic functions are investigated, and fundamental statistical measures extended according to neutrosophic logic are derived, such as the neutrosophic mathematical expectancy of multivariable neutrosophic vectors. Finally, the moment-generating function is examined from the perspective of extended neutrosophic logic and used as a powerful analytical tool for describing the linear structures of neutrosophic random variables. The aim of this study is to find a more flexible and accurate probabilistic environment for dealing with real-world phenomena where data are often unavailable, missing, or contain an aspect of indeterminacy, since neutrosophic logic relies in its study of phenomena on three aspects: the truth of the statement T, the falsity of the statement F, and the indeterminacy I