Research On The Topics Of Neutrosophic Operations Research

In this volume, we present a set of research that was published in cooperation with a number of researchers and those interested in keeping pace with the great scientific development that our contemporary world is witnessing, and one of its products was neutrosophic science, which was founded by the American scientist and mathematical philosopher Florentin Smarandache in 1995. Through it, we present a new vision for some research methods. Operations research to the concepts of this science.

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.

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.

This book treats all kind of data in neutrosophic environment, with real-life applications, approaching topics as linear programming problem, linear fractional programming, integer programming, triangular neutrosophic numbers, single valued triangular neutrosophic number, neutrosophic optimization, goal programming problem, Taylor series, multi-objective programming problem, neutrosophic geometric programming, neutrosophic topology, neutrosophic open set, neutrosophic semi-open set, neutrosophic continuous function, cylindrical skin plate design, neutrosophic MULTIMOORA, alternative solutions, decision matrix, ratio system, reference point method, full multiplicative form, ordinal dominance, standard error, market research, and so on. The selected papers deal with the alleviation of world changes, including changing demographics, accelerating globalization, rising environmental concerns, evolving societal relationships, growing ethical and governance concern, expanding the impact of technology; some of these changes have impacted negatively the economic growth of private firms, governments, communities, and the whole society.

This book treats all kind of data in neutrosophic environment, with reallife applications, approaching topics as logistic center, multi-criteria group decision making, hybrid score-accuracy function, single valued neutrosophic set, single valued neutrosophic number, neutrosophic MOORA, supplier selection, neutrosophic crisp sets, analytic network process, neutrosophic set, multi-criteria decision analysis (MCDM), complex neutrosophic set, interval complex neutrosophic set, interval complex neutrosophic graph of type 1, adjacency matrix, and so on.

Simulation is a numerical technique used to perform tests on a numerical computer, and involves logical and mathematical relationships interacting with each other to describe the behavior and structure of a complex system in the real world over a period of time. Analysis using simulation is a "natural" and logical extension of the mathematical analytical models inherent in operations research, because most operations research methods depend on building mathematical models that closely approximate the real-world environment and we obtain the optimal solution for them using algorithms appropriate to the type of these models. The importance of the simulation process comes in all branches of science, there are many systems that cannot be studied directly, due to the great difficulty that we may encounter when studying, and the high cost, in addition to the fact that some systems cannot be studied directly. The simulation process depends on generating a series of numbers. Randomness subject to a uniform probability distribution over the domain [0,1] , then converting these numbers into random variables subject to the law of probability distribution by which the system to be simulated works, using known transformation methods.

This book treats all kind of data in neutrosophic environment, with real-life applications, approaching topics as linear programming problem, linear fractional programming, integer programming, triangular neutrosophic numbers, single valued triangular neutrosophic number, neutrosophic optimization, goal programming problem, Taylor series, multi-objective programming problem, neutrosophic geometric programming, neutrosophic topology, neutrosophic open set, neutrosophic semi-open set, neutrosophic continuous function, cylindrical skin plate design, neutrosophic MULTIMOORA, alternative solutions, decision matrix, ratio system, reference point method, full multiplicative form, ordinal dominance, standard error, market research, and so on. The selected papers deal with the alleviation of world changes, including changing demographics, accelerating globalization, rising environmental concerns, evolving societal relationships, growing ethical and governance concern, expanding the impact of technology; some of these changes have impacted negatively the economic growth of private firms, governments, communities, and the whole society.

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming.