International Journal of Neutrosophic Science

  Reliability is one of the most important indicators of the quality of any system or product, ranging from the simplest machines as a product in any factory to the most complex system, such as phone or aircraft or missile engines, etc. The accuracy of these products indicates their high reliability, and therefore the customer or business owner will have confidence in products and will request more quantity. To reach the highest level of accuracy for the reliability of any system, the corresponding data must be very accurate. For this purpose, we proposed to add accuracy to reliability by adding data that contains more pieces of information about a  specific product or problem. We introduced a new logic (Neutrosophic logic) of data instead of classical logic which gives us more accuracy of data that contain indeterminacy such as extremist, vague, and unclear data. We defined the neutrosophic reliability according to the modern neutrosophic logic by constructing a neutrosophic reliability function. We have used the type of series as an application of neutrosophic reliability and introduced some examples. Neutrosophic reliability theory can be applied in computer science and decision support systems.  

  This paper is dedicated to study the n-refined neutrosophic linear Diophantine equations. It provides for the first time an easy algorithm to solve these equations, with many related examples.  

  In this paper, the Bernoulli’s neutrosophic differential equations by a neutrosophic thick function are introduced.The main objective is defining a neutrosophic differential equations that translate into linear based on the thick function and finding solutions for this equation. Enough examples are provided to illustrate each idea.  

    This paper dedicated to defining for the first time the concept of complex refined neutrosophic numbers as a direct application of refined neutrosophic sets and as a new generalization of neutrosophic complex numbers. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations. The importance of the definitions in this article lies in the use of them by defining the polar form of the refined neutrosophic complex numbers.      

  This paper introduces for the first time the concept of n-cyclic refined neutrosophic group as a direct application of the concept of n-cyclic refined neutrosophic set. Also, it discusses some of its elementary properties such as AH-subgroups, kernels, and direct products.