We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components, while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept.
The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.
In this paper we try to introduce neutrosophic bitopological group. We try to investigate some new definition and properties of neutrosophic bitopological group.
In this chapter, we introduce neutrosophic triplet cosets for neutrosophic triplet G-module and neutrosophic triplet quotient G-module. Then, we give some definitions and examples for neutrosophic triplet quotient G-module and neutrosophic triplet cosets. Also, we obtain isomorphism theorems for neutrosophic triplet G-modules and we prove isomorphism theorems for neutrosophic triplet G-modules.
In this paper, we examine the group structure of single valued neutrosophic sets. We introduce an approach to neutrosophic subgroup and establish some of its basic properties and characterizations. Then we give the homomorphic image and preimage of a neutrosophic (normal) subgroup.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.
This volume is a collection of ten papers, written by different authors and co-authors (listed in the order of the papers): F. Smarandache, Jun Ye, M. Shabir, M. Ali, M. Naz, F. Yuhua, A. A. Salama, S. Vladutescu, Y. Guo, A. Sengur, S. Broumi, P. Chi, and P. Liu. In first paper, the author proposed Neutrosophic Measure and neutrosophic Integral. Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Multiple Attribute Decision-Making Method is proposed in the second paper. Soft Neutrosophic Group is studied in third paper. In fourth paper Neutrosophic Example in Physics is discussed. Similarly in fifth paper Filters via Neutrosophic Crisp Sets are discussed. In paper six, Commnication vs. Information, an Axiomatic Neutrosophic Solution is presented by the authors. A Novel Image Segmentation Algorithm Based on Neutrosophic Filtering and Level Set is given in seventh paper. Paper eight is about to Neutrosophic Crisp Points and Neutrosophic Crisp Ideals. In the next paper Several Similarity Measures of Neutrosophic Sets are discussed. The authors introduced An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Sets in the last paper.
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
The objective of this paper is to introduce the concept of neutrosophic nearrings. The concept of neutrosophic N-group of a neutrosophic nearring is introduced. We study neutrosophic subnearrings of neutrosophic nearrings and also neutrosophic N-subgroups of neutrosophic N- groups.
Research on algebraic structure of group rings is one of the leading, most sought-after topics in ring theory. The new class of neutrosophic rings defined in this book form a generalization of group rings and semigroup rings.The study of the classes of neutrosophic group neutrosophic rings and S-neutrosophic semigroup neutrosophic rings which form a type of generalization of group rings will throw light on group rings and semigroup rings which are essential substructures of them. A salient feature of this group is the many suggested problems on the new classes of neutrosophic rings, solutions of which will certainly develop some of the still open problems in group rings.Further, neutrosophic matrix rings find applications in neutrosophic models like Neutrosophic Cognitive Maps (NCM), Neutrosophic Relational Maps (NRM), Neutrosophic Bidirectional Memories (NBM) and so on.
