Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments
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 ∈ ℝ), this paper introduces some basic operations of NNs and concepts of NN nonlinear functions and...
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| Format: | Article |
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MDPI AG
2018-02-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/1/13 |
| _version_ | 1818942702380646400 |
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| author | Jun Ye Wenhua Cui Zhikang Lu |
| author_facet | Jun Ye Wenhua Cui Zhikang Lu |
| author_sort | Jun Ye |
| collection | DOAJ |
| description | 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 ∈ ℝ), 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. |
| first_indexed | 2024-12-20T07:15:38Z |
| format | Article |
| id | doaj.art-3547be2977f54a4ba83d14d06129df8c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-20T07:15:38Z |
| publishDate | 2018-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3547be2977f54a4ba83d14d06129df8c2022-12-21T19:48:48ZengMDPI AGAxioms2075-16802018-02-01711310.3390/axioms7010013axioms7010013Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number EnvironmentsJun Ye0Wenhua Cui1Zhikang Lu2Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaDepartment of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaDepartment of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaIn 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 ∈ ℝ), 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.http://www.mdpi.com/2075-1680/7/1/13neutrosophic numberneutrosophic number functionneutrosophic number nonlinear programmingneutrosophic number optimal solution |
| spellingShingle | Jun Ye Wenhua Cui Zhikang Lu Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments Axioms neutrosophic number neutrosophic number function neutrosophic number nonlinear programming neutrosophic number optimal solution |
| title | Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments |
| title_full | Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments |
| title_fullStr | Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments |
| title_full_unstemmed | Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments |
| title_short | Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments |
| title_sort | neutrosophic number nonlinear programming problems and their general solution methods under neutrosophic number environments |
| topic | neutrosophic number neutrosophic number function neutrosophic number nonlinear programming neutrosophic number optimal solution |
| url | http://www.mdpi.com/2075-1680/7/1/13 |
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