Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability

TL;DR

This paper introduces the concepts of neutrosophic measure, integral, and probability, providing a new framework for handling indeterminacy distinct from randomness, with practical examples and flexible definitions.

Contribution

It develops the foundational notions of neutrosophic measure, integral, and probability, expanding the tools for modeling indeterminacy in various contexts.

Findings

Defined neutrosophic measure, integral, and probability

Presented practical examples illustrating neutrosophic concepts

Showed the flexibility in defining neutrosophic measures

Abstract

In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.