International Journal of Neutrosophic Science (IJNS) Vol. 1, No. 1, PP. 19-28, 2020 Doi :10.5281/zenodo.3679499 19 A Direct Model for Triangular Neutrosophic Linear Programming S. A. Edalatpanah 1* Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran Email: saedalatpanah@gmail.com Abstract This paper aims to propose a new direct algorithm to solve the neutrosophic linear programming where the variables and right-hand side represented with triangular neutrosophic numbers. The effectiveness of the proposed procedure is illustrated through numerical experiments. The extracted results show that the new algorithm is straightforward and could be useful to guide the modeling and design of a wide range of neutrosophic optimization. Keywords: Single valued neutrosophic number; Neutrosophic linear programming problem; Linear programming problem. 1. Introduction Fuzzy set originally introduced by Zadeh [1] in 1965 is a useful tool to capture the imprecision and uncertainty in decision-making [2, 3]. It is characterized by a membership degree between zero and one, and the non-membership degree is equal to one minus the membership degree. The intuitionistic fuzzy set (IFS) theory launched by Atanassov [4], addresses the problem of uncertainty by considering a non-membership function along with the fuzzy membership function on a universal set. The membership degree of an object is complemented with a non- membership degree that gives the extent to which an object does not belong to the IFS such that the sum of the two degrees should be less than or equal to 1. Neutrosophy has been proposed by Smarandache [5] as a new branch of philosophy, with ancient roots, dealing with “the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra”. The fundamental thesis of neutrosophy is that every idea has not only a certain degree of truth, as is generally assumed in many-valued logic contexts but also a falsity and indeterminacy degrees that have to be considered independently from each other. Smarandache seems to understand such “indeterminacy” both in a subjective and an objective sense, i.e., as uncertainty as well as imprecision, vagueness, error, doubtfulness, etc. Neutrosophic set (NS) is a generalization of the fuzzy set [1] and intuitionistic fuzzy set [4] and can deal with uncertain, indeterminate and incongruous information where the indeterminacy is quantified explicitly and truth membership, indeterminacy membership and falsity membership are completely independent. It can effectively describe uncertain, incomplete and inconsistent information and overcomes some limitations of the existing methods in depicting uncertain decision information. In the neutrosophic logic, each proposition is estimated by a triplet viz, truth grade, indeterminacy grade and falsity grade. The indeterministic part of uncertain data, introduced in NS theory, plays an important role in making a proper decision which is not possible by intuitionistic fuzzy set theory. Since indeterminacy always appears in our routine activities, the NS theory can analyze the various situations smoothly. Moreover, some extensions of NSs, including interval neutrosophic set [6], bipolar neutrosophic set [7], single-valued neutrosophic set [8], multi-valued neutrosophic set [9], and neutrosophic linguistic set [10] have been proposed and applied to solve various problems [11-20].