Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

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 information technology, the concepts of cost, time, delivery, space, quality, durability, and price have gained greater importance in solving managerial decision-making problems in supply chain models, transportation problems, and inventory control problems. Moreover, competition is becoming tougher in imprecise environments. Neutrosophic sets and logic are gaining significant attention in solving real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. Neutrosophic Sets in Decision Analysis and Operations Research is a critical, scholarly publication that examines various aspects of organizational research through mathematical equations and algorithms and presents neutrosophic theories and their applications in various optimization fields. Featuring a wide range of topics such as information retrieval, decision making, and matrices, this book is ideal for engineers, technicians, designers, mathematicians, practitioners of mathematics in economy and technology, scientists, academicians, professionals, managers, researchers, and students.

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory.

Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics investigates and presents the many applications that have arisen in the last ten years using neutrosophic statistics in bioinformatics, medicine, agriculture and cognitive science. This book will be very useful to the scientific community, appealing to audiences interested in fuzzy, vague concepts from which uncertain data are collected, including academic researchers, practicing engineers and graduate students. Neutrosophic statistics is a generalization of classical statistics. In classical statistics, the data is known, formed by crisp numbers. In comparison, data in neutrosophic statistics has some indeterminacy. This data may be ambiguous, vague, imprecise, incomplete, and even unknown. Neutrosophic statistics refers to a set of data, such that the data or a part of it are indeterminate in some degree, and to methods used to analyze the data.

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.

Optimization Theory Based on Neutrosophic and Plithogenic Sets presents the state-of-the-art research on neutrosophic and plithogenic theories and their applications in various optimization fields. Its table of contents covers new concepts, methods, algorithms, modelling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, nonlinear problems and new information related to optimization for the topic from the theoretical and applied viewpoints in neutrosophic sets and logic.

NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

In information technology, the concepts of cost, time, delivery, space, quality, durability, and price have gained greater importance in solving managerial decision-making problems in supply chain models, transportation problems, and inventory control problems. Moreover, competition is becoming tougher in imprecise environments. Neutrosophic sets and logic are gaining significant attention in solving real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. Neutrosophic Sets in Decision Analysis and Operations Research is a critical, scholarly publication that examines various aspects of organizational research through mathematical equations and algorithms and presents neutrosophic theories and their applications in various optimization fields. Featuring a wide range of topics such as information retrieval, decision making, and matrices, this book is ideal for engineers, technicians, designers, mathematicians, practitioners of mathematics in economy and technology, scientists, academicians, professionals, managers, researchers, and students.

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory.

Written by 13 contributors from different regions of the World, this book is a collection of papers written by researchers who have been working toward defining new concepts in the sciences for years. Among the new approaches, new views have been developed based on the emerging mathematical principles, the observation of possible relationships between physical processes, and ideas inspired by firsthand experience penetrating elusive realms. In the frame of the new explanatory theoretic models, matter and energy may be different characteristics of a physical system and "equivalence" between matter and energy becomes not so obvious. Quantum Mechanics was developed based on the assumption that electron mass is constant. Variable electron mass automatically rules out the entirety of quantum mechanics. Electron mass can change during chemical and biological processes and then other characteristics modify correspondingly. It is accepted that the Special Theory of Relativity (STR) does not contradict quantum mechanics, but in reality, the opposite is true. Even for a non-rocket scientist, this contradiction becomes evident with the simplest analysis of energy mass and energy equivalence formula. In simple words, the formula assumes that if energy is quantised, mass must be quantized too. How do atomic particles know how much mass to convert into energy and keep the same proportion in the conversion? Maybe one proton or one neutron converts more mass than his neighbor does! If protons and neutrons can be fragmented and divided using the MeV energy order, then why do we need CERN or other large nuclear facilities? Contributors of this volume: George Shpenkov. Institute of Mathematics & Physics, UTA, Bydgoszcz, Poland; Leonid Kreidik. Minsk, Belarus; Volodymyr Krasnoholovets. Senior Research Scientist, Department of Theoretical Physics, Institute of Physics, National Academy of Sciences of Ukraine. Kyiv, Ukraine; Victor Christianto. Malang Institute of Agriculture (IPM), Indonesia; Florentin Smarandache. Chair of Mathematics and Sciences, University of New Mexico, New Mexico, USA. Gallup, New Mexico 87301, USA; Robert Neil Boyd. Consulting physicist for Princeton Biotechnology Corporation, Dept. Information Physics Research; Adrian Klein. Cognitive neuropsychology, PhD Metaphysical sciences, Parapsychological Association, ECAO, ISPE, IQN, AAPS, AAAS. Affiliation: ECAO Aff., Israel; Akira Kanda. Professor of Mathematics and Logic. Omega Mathematical Institute; Mihai Prunescu. University of Bucharest; Renata Wong. Nanjing University, China; Arnold Gorgels. Mathematical Physics, Institute in Potsdam, Member DPG, Germany; Ying-Qiu Gu. School of Mathematical Science, Fudan University, China.

Contributing to the fast-growing new field of neutrosophy, this book provides a significant collection of inedited articles covering the latest ongoing research area. Neutrosopy is above all a new view on modelling, tailored to effectively address the uncertainties inherent to the real world. In short, neutrosophy supersedes in logics the binary approach of true or false by introducing a third state: neutral, which can be also interpreted as indeterminate, uncertain and inconsistent. Development of neutrosophy, since its conception by Smarandache in 1988, has grown exponentially by conceptual extensions to logics, measure, sets, graphs, as well as practical applications in namely all fields. It can be thought of as a generalization of fuzzy logic and its variants like intuitionistic fuzzy logic. Registered in a wide collection of books on this promising field, here we deliver to researchers, lecturers and postgraduate students pursuing research on neutrosophic, a set of eighteen unreleased articles on state-of-the-art theoretical developments, applications and understanding of neutrosophy. This volume complements the reference works of the founder and extends the already numerous books of him and other researchers on the subject. This book starts by describing in an application major step for product acceptance determination using similarity measure index by applying neutrosophic statistics. In one of the latest major mathematics branches, graph theory, we provide an article on neutrosophic extension of graphs that we can call a neutrosophic graph. A reflection is given on the true nature of neutrosophy by exploring its link with learning such as by Artificial Neural Networks, including Deep Learning. Again in mathematics a discussion is made on the solving of system of linear equations in neutrosophic representation. We also go to the opposite end of the theory, down to the practical details of implementation of topology using the C# language. Neutrosophic probability is another big new research field. Here we give a study on the advantages of using neutrosophic variables. Other disciplines such as algebraic structures, topological spaces, and decision-making as well as problems in logistics and transport are covered by the remaining articles. Last but not least, a major paper is given, that concludes this short presentation of our book, " When Neutrosophic Theory Meets Three-Way Decisions ".

Society forges ahead in the process of solving various contradictory problems and it is ceaselessly innovating. It is the desire of mankind to use computers and computing networks to help deal with contradictory problems and to conduct innovative activities. Using formal models to discuss object extension and the possibility of change, as well as the rules and methods for innovation, Extenics is applied to solving contradictory problems and has become the basic theory, method and instrument to achieve this goal. In the 30 years since the foundation of Extenics, researchers have built relatively complete theoretical systems -'extension theory', studied formal and modeling innovation methods -'extension innovation methods', and launched the applications in various fields such as information, design, automation and management etc. -'extension engineering'. Extension theory, the extension innovation method and extension engineering jointly constitute the new discipline-Extenics. At the same time, the practical activities of engineering technology and management promote the integration of various innovation methods such as TRIZ and brainstorming etc. This book collects together, from scholars in various fields, the research achievements in Extenics and innovation methods, in order to facilitate and promote the development of Extenics and the various innovation theories and methods, as well as to improve its innovative capacity in academic and business circles.