Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility

  • Authors:

  • Masatoshi Sakawa;Hideki Katagiri;Takeshi Matsui

  • Affiliations:

  • Department of Cybernetics Systems, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan;Department of Cybernetics Systems, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan;Department of Cybernetics Systems, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.