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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Bibliographic Details
Published in:Expert systems with applications Vol. 40; no. 2; pp. 563 - 574
Main Authors: Katagiri, Hideki, Uno, Takeshi, Kato, Kosuke, Tsuda, Hiroshi, Tsubaki, Hiroe
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.02.2013
Elsevier
Subjects:
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
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
ISSN:0957-4174, 1873-6793
Online Access:Get full text
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Summary:► 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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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2012.07.064