On the analytic representation of the Leximin ordering and its application to flexible constraint propagation

On the analytic representation of the Leximin ordering and its application to flexible constraint propagation

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Article ID: iaor19991944
Country: Netherlands
Volume: 102
Issue: 1
Start Page Number: 176
End Page Number: 192
Publication Date: Oct 1997
Journal: European Journal of Operational Research
Authors:
Keywords: programming: mathematical
Abstract:

We discuss the basic formulation of constraint propagation problems and extend it to the flexible constraint propagation environment where constraints are represented as fuzzy subsets. Some methods for ordering alternative solutions with respect to a collection of flexible constraints are discussed along with their drawbacks. Among the methods introduced is the Leximin method where we note its lack of an analytic formulation. With the aid of the ordered weighted averaging operator we suggest an analytic formulation for the Leximin method. Some properties of this formulation are provided. We then describe the application of this new formulation for the Leximin method to situations in which the constraints are describable in a linear fashion. We show how we can use mixed integer programming techniques to find an optimal solution.

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