Abstract
A neutrosophic number (NN) presented by Smarandache can express determinate and/or indeterminate information in real life. NN (z = a + uI) consists of the determinate part a and the indeterminate part uI for a, u ∈ R (R is all real numbers) and indeterminacy I, and is very suitable for representing and handling problems with both determinate and indeterminate information. Based on the concept of NNs, this paper presents for first time the concepts of neutrosophic linear equations and the neutrosophic matrix, and introduces the neutrosophic matrix operations. Then, we propose some solving methods, including the substitution method, the addition method, and the inverse matrix method, for the system of neutrosophic linear equations or the neutrosophic matrix equation. Finally, an applied example about a traffic flow problem is provided to illustrate the application and effectiveness of handling the indeterminate traffic flow problem by using the system of neutrosophic linear equations.
Highlights
The condensed traffic flow along with the increasing number of vehicles is increasingly complex and uncertain in actual road traffic situations [1]
It is obvious that existing fuzzy sets/numbers cannot express neutrosophic linear equations with both determinate and indeterminate information (NNs)
In this paper, based on neutrosophic number (NN) we propose for the first time the new concepts of neutrosophic linear equations and the neutrosophic matrix, and the solving methods of the system of neutrosophic linear equations by using the substitution method, the addition method, and the inverse matrix method
Summary
The condensed traffic flow along with the increasing number of vehicles is increasingly complex and uncertain in actual road traffic situations [1]. The neutrosophic functions introduced in [12,13] are interval functions (thick function), but they cannot express and handle actual problems containing NN information. It is obvious that existing fuzzy sets/numbers cannot express neutrosophic linear equations with both determinate and indeterminate information (NNs). In this paper, based on NNs we propose for the first time the new concepts of neutrosophic linear equations and the neutrosophic matrix, and the solving methods of the system of neutrosophic linear equations by using the substitution method, the addition method, and the inverse matrix method.
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