Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)
► We tackle a new multiobjective programming problem with random fuzzy variables. ► We propose a new model optimizing possibilistic value at risk, called pVaR. ► We prove that the original problem can be transformed into a deterministic problem. ► We provide an interactive algorithm to obtain a sati...
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| Published in: | Expert systems with applications Vol. 40; no. 2; pp. 563 - 574 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.02.2013
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| ISSN: | 0957-4174, 1873-6793 |
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| Abstract | ► We tackle a new multiobjective programming problem with random fuzzy variables. ► We propose a new model optimizing possibilistic value at risk, called pVaR. ► We prove that the original problem can be transformed into a deterministic problem. ► We provide an interactive algorithm to obtain a satisficing solution. ► Our algorithm can exactly obtain Pareto optimal solutions using a convex property.
This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments. |
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| AbstractList | ► We tackle a new multiobjective programming problem with random fuzzy variables. ► We propose a new model optimizing possibilistic value at risk, called pVaR. ► We prove that the original problem can be transformed into a deterministic problem. ► We provide an interactive algorithm to obtain a satisficing solution. ► Our algorithm can exactly obtain Pareto optimal solutions using a convex property.
This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments. This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments. |
| Author | Tsuda, Hiroshi Kato, Kosuke Uno, Takeshi Tsubaki, Hiroe Katagiri, Hideki |
| Author_xml | – sequence: 1 givenname: Hideki surname: Katagiri fullname: Katagiri, Hideki email: katagiri-h@hiroshima-u.ac.jp organization: Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8527, Japan – sequence: 2 givenname: Takeshi surname: Uno fullname: Uno, Takeshi email: uno@ias.tokushima-u.ac.jp organization: Institute of Socio-Arts and Sciences, The University of Tokushima, 1-1, Minamijosanjima-cho, Tokushima-shi, Tokushima 770-8502, Japan – sequence: 3 givenname: Kosuke surname: Kato fullname: Kato, Kosuke email: k.katoh.me@it-hiroshima.ac.jp organization: Faculty of Applied Information Science, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan – sequence: 4 givenname: Hiroshi surname: Tsuda fullname: Tsuda, Hiroshi email: htsuda@mail.doshisha.ac.jp organization: Faculty of Science and Engineering, Doshisya University, Tatara Miyakodani 1-3, Kyotanabe City 610-0394, Japan – sequence: 5 givenname: Hiroe surname: Tsubaki fullname: Tsubaki, Hiroe email: tsubaki@ism.ac.jp organization: Department of Data Science, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan |
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| Keywords | Possibilistic value at risk (pVaR) Interactive algorithm Necessity Pareto optimal solution Multiobjective linear programming Possibility Random fuzzy variable Multiobjective programming Financial management Convex programming Optimization Uncertain system Possibility theory Angular distribution Deterministic approach Quantile Random variable Interactive programming Warranty Probabilistic approach Pareto optimum Decision support system Decision making Linear programming Fuzzy programming Risk analysis Fuzzy logic Optimal solution Objective function Risk management Portfolio management |
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| Snippet | ► We tackle a new multiobjective programming problem with random fuzzy variables. ► We propose a new model optimizing possibilistic value at risk, called pVaR.... This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A... |
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| SubjectTerms | Applied sciences Decision theory. Utility theory Exact sciences and technology Fuzzy Fuzzy logic Fuzzy set theory Interactive algorithm Mathematical analysis Mathematical models Mathematical programming Multiobjective linear programming Necessity Operational research and scientific management Operational research. Management science Optimization Pareto optimal solution Pareto optimality Portfolio theory Possibilistic value at risk (pVaR) Possibility Random fuzzy variable Risk Risk theory. Actuarial science |
| Title | Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR) |
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