Studies of stochastic programming models using possibility and necessity measures for linear programming problems with fuzzy random variable coefficients

Abstract

AbstractThis paper considers the multi‐objective linear programming problem and discusses the case in which the coefficients of the objective function are fuzzy random variables. First, the fuzzy goal is introduced into the objective function, considering the fuzzy decision of the human decision‐maker. We consider a model in which the possibility or the necessity that the objective function value achieves the fuzzy goal is maximized on the basis of fuzzy programming or possibility programming. It is noted that the possibility or necessity fluctuates stochastically, and a decision‐making process based on the stochastic programming model is proposed. After modifying the problem with constraint into an equivalent deterministic problem, the convex programming problem with a parameter is introduced. Then, an algorithm is proposed in which the optimal solution is derived, combining nonlinear programming and the bisection method. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(1): 68–75, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10151