A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees.

This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings.

Neutrosophic Set in Medical Image Analysis gives an understanding of the concepts of NS, along with knowledge on how to gather, interpret, analyze and handle medical images using NS methods. It presents the latest cutting-edge research that gives insight into neutrosophic set's novel techniques, strategies and challenges, showing how it can be used in biomedical diagnoses systems. The neutrosophic set (NS), which is a generalization of fuzzy set, offers the prospect of overcoming the restrictions of fuzzy-based approaches to medical image analysis. - Introduces the mathematical model and concepts of neutrosophic theory and methods - Highlights the different techniques of neutrosophic theory, focusing on applying the neutrosophic set in image analysis to support computer- aided diagnosis (CAD) systems, including approaches from soft computing and machine learning - Shows how NS techniques can be applied to medical image denoising, segmentation and classification - Provides challenges and future directions in neutrosophic set based medical image analysis

This Special Issue presents original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.

In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information.

In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations.

A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees.