Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We rst introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We de ne bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.

This monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar information—positive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.

This book addresses single-valued neutrosophic graphs and their applications. In addition, it introduces readers to a number of central concepts, including certain types of single-valued neutrosophic graphs, energy of single-valued neutrosophic graphs, bipolar single-valued neutrosophic planar graphs, isomorphism of intuitionistic single-valued neutrosophic soft graphs, and single-valued neutrosophic soft rough graphs. Divided into eight chapters, the book seeks to remedy the lack of a mathematical approach to indeterminate and inconsistent information. Chap. 1 presents a concise review of single-valued neutrosophic sets, while Chap. 2 explains the notion of neutrosophic graph structures and explores selected properties of neutrosophic graph structures. Chap. 3 discusses specific bipolar neutrosophic graphs. Chap. 4 highlights the concept of interval-valued neutrosophic graphs, while Chap. 5 presents certain notions concerning interval-valued neutrosophic graph structures. Chap. 6 addresses the concepts of rough neutrosophic digraphs and neutrosophic rough digraphs. Chap. 7 focuses on the concepts of neutrosophic soft graphs and intuitionistic neutrosophic soft graphs, before Chap. 8 rounds out the book by considering neutrosophic soft rough graphs.

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

This is the second volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to my invitation. The introduction contains a short history of neutrosophics, together with links to the main papers and books.

This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before.

In this research article, we present certain notions of bipolar neutrosophic graphs. We study the dominating and independent sets of bipolar neutrosophic graphs. We describe novel multiple criteria decision making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs.