Interactive Decision Making for Multiobjective Simple Recourse Programming Problems with Discrete or Continuous Fuzzy Random Variables

  • Hitoshi YanoEmail author
  • Rongrong Zhang
Conference paper


In this paper, we formulate multiobjective simple recourse programming problems in which discrete fuzzy random variables or continuous ones are involved in equality constraints. In the proposed methods, equality constraints with two types of fuzzy random variables are defined on the basis of a possibility measure and and a two-stage programming method. For a given permissible possibility level specified by the decision maker, a Pareto optimality concept is introduced. Both an interactive linear programming algorithm for discrete fuzzy random variables and an interactive convex programming algorithm for continuous fuzzy random variables are developed to obtain a satisfactory solution from among a Pareto optimal solution set. The proposed methods are applied to farm planning problems in the Philippines, in which it is assumed that the amount of water supply in dry season is represented as a discrete fuzzy random variable or a continuous one.


Programming Problem Equality Constraint Pareto Optimal Solution Reference Objective Satisfactory Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J.R. Birge, F. Louveaux, Introduction to Stochastic Programming (Springer, New York/Berlin, 1997)zbMATHGoogle Scholar
  2. 2.
    A. Charnes, W.W. Cooper, Chance constrained programming. Manag. Sci. 6, 73–79 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    G.B. Danzig, Linear programming under uncertainty. Manag. Sci. 1, 197–206 (1955)MathSciNetCrossRefGoogle Scholar
  4. 4.
    D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications (Academic, New York, 1980)zbMATHGoogle Scholar
  5. 5.
    G.H. Huang, D.P. Louck, An inexact two-stage stochastic programming model for water resources management under uncertainty. Civ. Eng. Environ. Syst. 17, 95–118 (2000)CrossRefGoogle Scholar
  6. 6.
    P. Kall, J. Mayer, Stochastic Linear Programming Models, Theory, and Computation (Springer, Boston, 2005)zbMATHGoogle Scholar
  7. 7.
    H. Katagiri, M. Sakawa, K. Kato, S. Ohsaki, An interactive fuzzy satisficing method for fuzzy random multiobjective linear programming problems through the fractile optimization model using possibility and necessity measures, in Proceedings of the Ninth Asia Pacific Management Conference, Osaka (2003), pp. 795–802Google Scholar
  8. 8.
    H. Katagiri, M. Sakawa, K. Kato, I. Nishizaki, Interactive multiobjective fuzzy random linear programming: maximization of possibility and probability. Eur. J. Oper. Res. 188, 530–539 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    H. Kwakernaak, Fuzzy random variables-I. Inf. Sci. 15, 1–29 (1978)CrossRefzbMATHGoogle Scholar
  10. 10.
    I. Maqsood, G.H. Huang, Y.F. Huang, ITOM: an interval parameter two-stage optimization model for stochastic planning of water resources systems. Stoch. Env. Res. Risk A 19, 125–133 (2005)CrossRefzbMATHGoogle Scholar
  11. 11.
    M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization (Plenum Press, New York/London, 1993)CrossRefzbMATHGoogle Scholar
  12. 12.
    M. Sakawa, T. Matsui, Interactive fuzzy multiobjective stochastic programming with simple recourse. Int. J. Multicrit. Decis. Mak. 4, 31–46 (2014)CrossRefzbMATHGoogle Scholar
  13. 13.
    M. Sakawa, I. Nishizaki, H. Katagiri, Fuzzy Stochastic Multiobjective Programming (Springer, New York, 2011)CrossRefzbMATHGoogle Scholar
  14. 14.
    M. Sakawa, H. Yano, I. Nishizaki, Linear and Multiobjective Programming with Fuzzy Stochastic Extensions (Springer, Boston, 2013)CrossRefzbMATHGoogle Scholar
  15. 15.
    W. Sun, C. An, G. Li, Y. Lv, Applications of inexact programming methods to waste management under uncertainty: current status and future directions. Environ. Syst. Res. 3, 1–15 (2014)CrossRefGoogle Scholar
  16. 16.
    D.W. Walkup, R. Wets, Stochastic programs with recourse. SIAM J. Appl. Math. 15, 139–162 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    R. Wang, Y. Li, Q. Tan, A review of inexact optimization modeling and its application to integrated water resources management. Front. Earth Sci. 9, 51–64 (2015)CrossRefGoogle Scholar
  18. 18.
    R. Wets, Stochastic programs with fixed recourse: the equivalent deterministic program. SIAM Rev. 16, 309–339 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    H. Yano, A formulation of fuzzy random simple recourse programming problems. Jpn. Soc. Fuzzy Theory Intell. Inf. 27, 695–699 (2015, In Japanese)Google Scholar
  20. 20.
    H. Yano, R. Zhang, Interactive decision making for multiobjective fuzzy random simple recourse programming problems and its application to rainfed agriculture in Philippines, in Proceedings of the International Multiconference of Engineers and Computer Scientists 2016, IMECS 2016, 16–18 Mar 2016, Hong Kong. Lecture Notes in Engineering and Computer Science, pp. 912–917Google Scholar
  21. 21.
    S. Yokoyama, S.R. Francisco, T. Nanseki, Optimum crop combination under risk: second cropping of paddy fields in the Philippines. Technol. Dev. Jpn. Int. Coop. Agency (JICA) 12, 65–74 (1999)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Graduate School of Humanities and Social SciencesNagoya City UniversityNagoyaJapan

Personalised recommendations