Preference Learning Based Decision Map Algebra: Specification and Implementation

Abstract

Decision Map Algebra (DMA) is a generic and context independent algebra, especially devoted to spatial multicriteria modelling. The algebra defines a set of operations which formalises spatial multicriteria modelling and analysis. The main concept in DMA is decision map, which is a planar subdivision of the study area represented as a set of non-overlapping polygonal spatial units that are assigned, using a multicriteria classification model, into an ordered set of classes. Different methods can be used in the multicriteria classification step. In this paper, the multicriteria classification step relies on the Dominance-based Rough Set Approach (DRSA), which is a preference learning method that extends the classical rough set theory to multicriteria classification. The paper first introduces a preference learning based approach to decision map construction. Then it proposes a formal specification of DMA. Finally, it briefly presents an object oriented implementation of DMA.