Fuzzy Analytical Hierarchial Processes

Abstract

Many problems in decision making structure reality into constituent parts, that is, into hierarchial charts in which the goal is at the top, while the decisions are at the lowest level of the chart. At the intermediate levels of the chart are the various attributes and/or conditions which must be considered in order to arrive at a decision. A rather simplified hierarchial chart is given, in which the goal, all attributes and all possible decisions occupy boxes in the hierarchial structure. The main idea in the Analytical Hierarchial Process (AHP) approach is to construct a pairwise ranking of the boxes at any given level relative to the boxes at the next highest level to which they are connected. These pairwise rankings are used to construct priorities which are then combined to create an overall priority for each course of action under consideration. The course of action with the highest priority is then chosen. Uncertainty in the assigning of priorities and the use of semantic variables in their assignment lead naturally to the inclusion of fuzzy logic into the structure of the AHP paradigm. In this paper we propose a method for using fuzzy sets in the context of the Analytical Hierarchial approach to decision making. A rather comprehensive example illustrates this method.