Interval Neutrosophic Sets

TL;DR

This paper introduces interval neutrosophic sets, a formal framework extending neutrosophic sets with set-theoretic operators, properties, and convexity, enhancing their mathematical foundation and applicability.

Contribution

It defines set-theoretic operators for interval neutrosophic sets, proves their properties, and establishes the convexity of these sets, advancing neutrosophic set theory.

Findings

Defined set-theoretic operators for INS

Proved properties related to INS operations and relations

Established the convexity of interval neutrosophic sets

Abstract

Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the set-theoretic operators on an instance of neutrosophic set, we call it interval neutrosophic set (INS). We prove various properties of INS, which are connected to the operations and relations over INS. Finally, we introduce and prove the convexity of interval neutrosophic sets.