Mysterious Neutrosophic Linear Models

Abstract

Operations research often shortened to the initialism O.R., is a discipline that deals with the development and application of advanced analytical methods to improve decision-making. It is sometimes considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. It has the ability to express the concepts of efficiency and scarcity in a well-defined mathematical model for a specific issue. It has the ability to use scientific methods to solve complex problems in managing large scale systems for factories, institutions, and companies, and enables them to make optimal scientific decisions for the functioning of Its work. Employing techniques from other mathematical sciences, such as modelling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries. The mathematical model is the simplified image of expressing a practical system from a real life problem or an idea put forward for an executable system, as the mathematical models consist of a goal function through which we search for the maximum or minimum value subject to restrictions. Linear mathematical programming is one of the most important topics in the field of operations research due to their frequent use in most areas of life. When studying linear programming, the first step is to identify the various types of linear models and how to transition from one to the next. We realize that the ideal solution of the linear model is influenced by the coefficients of the variables of objective function that describes a profit if the model is a maximizing model or represents a cost if the model is a minimization model, which is affected by environmental conditions. The fixed values that represent the right side of the inequalities (constraints), which express the available capital, time, raw resources, and so on, have an impact on the optimum solution. They are also affected by environmental conditions. We used to take these values as fixed values in classical logic, which does not correspond to reality and leads to erroneous solutions to the problems described by the linear model. As a result, it was essential to reformulate the classical linear models' problems, taking into consideration all probable scenarios and changes in the work environment. In this study, we will look into linear models and their kinds in view of neutrosophic logic, which takes into account all of the data and all of the changes that may occur in the issue under investigation, as well as the uncertainty that is encountered in the problem's data. We'll also look at it if the coefficients of the variables in the objective function are neutrosophic values, and the accessible options are neutrosophic values because we'll reformulate the existing linear mathematical models using neutrosophic logic, and show how to convert from one to another using some examples.