
doi: 10.1007/bf03398829
In this paper we study hierarchical systems with stochastic data: be it the cost coefficients, right-hand-side vector, coefficient matrix or any of their combinations. The problem is converted to its equivalent deterministic form using any known stochastic approach. This deterministic model (in case of a linear hierarchy) may be linear or nonlinear depending on which parameter in the problem is random. Finally the linear nonlinear deterministic model is solved using fuzzy technique [9] via linear membership function. We have also shown the application of the deterministic models to find a solution using numerical examples.
membership function, probabilistic bi-level programming problem, Fuzzy and other nonstochastic uncertainty mathematical programming, satisfactory solution, Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.), normal random variable(s), fuzzy programming
membership function, probabilistic bi-level programming problem, Fuzzy and other nonstochastic uncertainty mathematical programming, satisfactory solution, Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.), normal random variable(s), fuzzy programming
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