Neutrosophic number linear programming method and its application under neutrosophic number environments

In real world, there exists determinate and/or indeterminate information. Hence, the indeterminate problems are inevitable and have to be taken into account in optimization problems. Then, a neutrosophic number (NN) is very suitable for expressing determinate and/or indeterminate information because a NN (\(z=a + bI\)) consists of its determinate part a and its indeterminate part bI for \(a,b\in R\), where the symbol “I” denotes indeterminacy and R is all real numbers. This paper firstly presents some basic operations of NNs and a neutrosophic function involving NNs, which is simply called a NN function and then develops a NN linear programming (NNLP) method to handle NN optimization problems. Moreover, a numerical example and an application of production planning are provided, respectively, to show the solving method and application of NNLP problems. In general, the NNLP method yields the basic NN solutions. Further, the possible ranges of the optimal solution are discussed when the indeterminacy I is specified as a possible interval ranges corresponding to actual requirements in real applications.