Neutrosophic Statistics is an extension of Interval Statistics, while Plitogenic Statistics is the most general form of statistics (Fourth version)

Abstract

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions.

Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et al [1].

We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals.

We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses).