Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

  • Authors:

  • Hideki Katagiri;Takeshi Uno;Kosuke Kato;Hiroshi Tsuda;Hiroe Tsubaki

  • Affiliations:

  • Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8527, Japan;Institute of Socio-Arts and Sciences, The University of Tokushima, 1-1, Minamijosanjima-cho, Tokushima-shi, Tokushima 770-8502, Japan;Faculty of Applied Information Science, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan;Faculty of Science and Engineering, Doshisya University, Tatara Miyakodani 1-3, Kyotanabe City 610-0394, Japan;Department of Data Science, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2013

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Abstract

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.