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Axioms 2018, 7(1), 13; https://doi.org/10.3390/axioms7010013

Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments

Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
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Received: 22 January 2018 / Revised: 16 February 2018 / Accepted: 22 February 2018 / Published: 24 February 2018
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making)
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Abstract

In practical situations, we often have to handle programming problems involving indeterminate information. Building on the concepts of indeterminacy I and neutrosophic number (NN) (z = p + qI for p, q), this paper introduces some basic operations of NNs and concepts of NN nonlinear functions and inequalities. These functions and/or inequalities contain indeterminacy I and naturally lead to a formulation of NN nonlinear programming (NN-NP). These techniques include NN nonlinear optimization models for unconstrained and constrained problems and their general solution methods. Additionally, numerical examples are provided to show the effectiveness of the proposed NN-NP methods. It is obvious that the NN-NP problems usually yield NN optimal solutions, but not always. The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations. View Full-Text
Keywords: neutrosophic number; neutrosophic number function; neutrosophic number nonlinear programming; neutrosophic number optimal solution neutrosophic number; neutrosophic number function; neutrosophic number nonlinear programming; neutrosophic number optimal solution
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Ye, J.; Cui, W.; Lu, Z. Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments. Axioms 2018, 7, 13.

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