Construction of rule-based assignment models

Assignment refers to the problem of assigning objects or alternatives described on multiple dimensions into predefined categories. Most assignment models use analytical mechanisms to aggregate multiple dimensions in order to select a category for each candidate object. We investigate another approach based on the use of simple ‘if ... then ...’ rules. We propose a general approach for a progressive construction of a rule-based assignment model. The process consists of testing iteratively the consistency of the rule base to transform it progressively into a consistent assignment model. Consistency tests are based on a correspondence between the logical representation of rules and an equivalent algebraic representation. This allows us to express rules by linear constraints and then to test the consistency of rule-based assignment models by solving a series of linear programs.