A Novel Approach for Generalized Decagonal Neutrosophic Linear Programming Problem

In this manuscript, the author describes a new type of programming problem, i.e. decagonal neutrosophic linear programming problem (DgN-LPP), and proposes a novel solution methodology for DgN-LPP. To the best of our knowledge, this problem as well as the proposed solution technique have not been discussed in research literature so far. Decagonal neutrosophic numbers (DgNNs) are specific neutrosophic numbers (NNs) having a total of ten edges of all three parts of information viz. truthiness, falsity, and indeterminacy. Here, we formulate DgN-LPP as a linear programming problem with all its coefficients/ parameters in the form of Decagonal neutrosophic numbers (DgNNs). To design this problem, we elaborate on the different properties of decagonal neutrosophic numbers (DgNNs) and basic operations on two DgNNs. A new ranking function is also proposed to convert DgNNs into corresponding equivalent crisp values. With the help of the new ranking function, the current problem (DgN-LPP) is converted into an equivalent crisp LP problem. This crisp LP problem is solved with existing methods to obtain the optimal solution of the original DgN-LPP. A numerical example and a case study of an industrial production problem are illustrated to demonstrate the proposed solution techniques as well as their applicability in solving real problems.