Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables
This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/9/11/254 |
| _version_ | 1798004079861956608 |
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| author | Hideki Katagiri Kosuke Kato Takeshi Uno |
| author_facet | Hideki Katagiri Kosuke Kato Takeshi Uno |
| author_sort | Hideki Katagiri |
| collection | DOAJ |
| description | This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments. |
| first_indexed | 2024-04-11T12:17:53Z |
| format | Article |
| id | doaj.art-1344fff8c0e74f7cb60cbd9b26ed6219 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T12:17:53Z |
| publishDate | 2017-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1344fff8c0e74f7cb60cbd9b26ed62192022-12-22T04:24:12ZengMDPI AGSymmetry2073-89942017-10-0191125410.3390/sym9110254sym9110254Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random VariablesHideki Katagiri0Kosuke Kato1Takeshi Uno2Department of Industrial Engineering, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Yokohama-shi, Kanagawa 221-8686, JapanDepartment of Computer Science, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, JapanDepartment of Mathematical Science, Graduate School of Technology, Industrial and Social Science, Tokushima University, 2-1, Minamijosanjima-cho, Tokushima-shi, Tokushima 770-8506, JapanThis paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.https://www.mdpi.com/2073-8994/9/11/254discrete fuzzy random variablelinear programmingpossibility measurenecessity measureexpectation modelPareto optimal solution |
| spellingShingle | Hideki Katagiri Kosuke Kato Takeshi Uno Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables Symmetry discrete fuzzy random variable linear programming possibility measure necessity measure expectation model Pareto optimal solution |
| title | Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables |
| title_full | Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables |
| title_fullStr | Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables |
| title_full_unstemmed | Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables |
| title_short | Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables |
| title_sort | possibility necessity based probabilistic expectation models for linear programming problems with discrete fuzzy random variables |
| topic | discrete fuzzy random variable linear programming possibility measure necessity measure expectation model Pareto optimal solution |
| url | https://www.mdpi.com/2073-8994/9/11/254 |
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