A new approach to uncertain parameter linear programming

Abstract

A novel method for solving uncertain linear programming is put forward in this paper. In contrast to stochastic linear programming and most fuzzy linear programming models, the parameters of the problem discussed here are neither random variables with known probability distributions nor fuzzy parameters with known possibility distributions. All we know about the parameters is merely their intervals of existence. To solve this kind of uncertain linear programming might be very attractive since many actual decision problems could be formulated as such if we do not have enough information about the parameters. In this paper, the concept of a confidence function for inequalities is introduced. Based on this definition, the problem is solved by an iterative algorithm, then, the convergence of the algorithm is proved, and the decision risk grades for different confidence functions are discussed. Finally, an illustrative example is given to demonstrate the actual application of thismethod.