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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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Axioms 2018, 7(1), 13; https://doi.org/10.3390/axioms7010013
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)
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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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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Axioms, EISSN 2075-1680, Published by MDPI AG
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