Solving Neutrosophic Linear Programming Problems With Two-Phase Approach

Solving Neutrosophic Linear Programming Problems With Two-Phase Approach

Elsayed Metwalli Badr (Benha University, Egypt), Mustafa Abdul Salam (Benha University, Egypt) and Florentin Smarandache (University of New Mexico, USA)
Copyright: © 2020 |Pages: 22
DOI: 10.4018/978-1-7998-2555-5.ch016
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The neutrosophic primal simplex algorithm starts from a neutrosophic basic feasible solution. If there is no such a solution, we cannot apply the neutrosophic primal simplex method for solving the neutrosophic linear programming problem. In this chapter, the authors propose a neutrosophic two-phase method involving neutrosophic artificial variables to obtain an initial neutrosophic basic feasible solution to a slightly modified set of constraints. Then the neutrosophic primal simplex method is used to eliminate the neutrosophic artificial variables and to solve the original problem.
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2. Preliminaries

In this section, we introduce some basic definitions of the neutrosophic set theory.

Definition 1 [Abdel-Basset et al. 2018] A single-valued neutrosophic set N which is a subset of X is defined as follows:

where X is a universe of discourse,TN(x): X→[0,1], IN(x): X→[0,1] and FN(x): X→[0,1] with
for all xX, TN(x), IN(x) and FN(x) represent truth membership, indeterminacy membership and falsity membership degrees of x to N.

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