Ranking by AHP: a rough approach

Decision making is always a difficult assignment for everyone in every context and more information eases the process and makes it more accurate. More data does not always mean more information. Rough sets alone can be adopted to handle hierarchical structure in the family of criteria using decision rules based on preference model. The rules are induced from the preferential information given by the Decision Maker (DM) in the form of examples of decisions. The existing rough set techniques are applicable in information systems where condition and decision attributes are distinguishable. But, in general, the information are available in the form of a data table, called an information system or knowledge representation system, where rows are labeled by alternatives and columns by attributes. In such cases, the condition and decision attributes are not distinguishable. The present paper offers a solution for making decisions in an efficient way when enough data are available, relevant or irrelevant. In a Multiple Criteria Decision Analysis (MCDA) problem, determination of weights is an important aspect of the Analytic Hierarchy Process (AHP). Based on rough set concepts, a model, viz., the interval AHP model with interval data, for determination of the weights has been considered here. According to the necessary and possibility concepts of rough set, we obtain the lower and upper evaluation models, respectively. After obtaining the local interval weights, a method is proposed for calculating the global weights, and also for ranking the alternatives. The proposed method will be applicable for an information system as well as for a decision table.