Abstract
This paper extends the concept of crisp linear programming problem (lpp) by adopting the coefficients in objective function, technical coefficients, the right hand side coefficients and the decision variables as single valued triangular neutrosophic numbers (Sυtrn number). It is a special type of neutrosophic set. This modified concept is here called neutrosophic linear programming problem (Nlp problem). To develop this notion, a linear ranking function is newly constructed from geometrical concept first. Then the validity of existing crisp results are tested with the help of that ranking function in this new arena. An attempt is also taken to solve an Nlp problem by duality approach. For that, an efficient solution algorithm is developed by obeying the properties of ranking function. Finally, this proposed algorithm is demonstrated to solve a real life problem and some special cases are also illustrated by numerical examples.
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