Simulation of the Delphi Method with a Fuzzy Expert System

The introduction of fuzzy logic into expert systems is an approach that allows expert systems to deal with real-world aspects that cannot be modeled accurately with classical crisp logic. An example is the formation of human opinions that are not always crisp with respect to the membership of a certain element in a set. In addition, the Delphi method is a technique for forming a stable consensus from several opinions over several rounds during which experts may change their opinions. In contemporary approaches, the application of expert systems in most cases is not possible for the roundbased Delphi method. The contribution presented here addresses this problem, proposing a method for combining both techniques. As a result, the system Fuzzy Expert was created, a tool that comprises three functions: (1) modeling fuzzy sets, (2) modeling and evaluating fuzzy expert systems, and (3) simulating a round-based Delphi method by using several fuzzy expert systems. INTRODUCTION AND PROBLEM STATEMENT Expert systems are knowledge and rule based systems, which allow drawing conclusions on the basis of logical rules and facts (Jackson 1990). Introducing the theory of fuzzy sets (Zadeh 1965) into expert systems extends the modeling capabilities of these systems. With fuzzy sets, situations can be modeled where a certain statement is true to some degree in between the two extremes “true” and “false”. This is particularly useful as human opinions are not always sharply defined values in the sense of the classical logic. Fuzzy expert systems allow fuzzy operators for combining conditions within rules, for combining rules, and they allow fuzzy membership functions of various types to describe set membership. The Delphi method, developed in the 1950s at RAND Corp. (Helmer 1967), is a technique for combining the opinions of several experts in a round-based survey to form a group opinion. It borrows its name from the famous oracle, since its main application is the prediction of future developments. usually the Delphi method is applied to the opinions of human experts who communicate between the rounds of the survey and give feedback about the preceding rounds. The experts then revise their opinions based on the feedback information. Several variations of the Delphi method exist, (see Rowe and Wright 1999). Among all methods, there are four key features, which characterize a method as a Delphi method: “anonymity, iteration, controlled feedback, and a statistical aggregation of group response” (Rowe and Wright 1999). Anonymity means that after a round is completed, all participating experts get the accumulated results of the round as a feedback, but without knowing the contributions of the single experts. Iteration refers to several rounds that are executed subsequently. Controlled feedback refers to the possibility of the experts to get aware of the opinion of their anonymous colleagues. This may be statistically aggregated information of the results from the last rounds, or, in some cases, it may even include rationales for individual opinions. The final result is a statistically aggregated result from the last iteration. Several extensions of the Delphi method have proposed to use fuzzy logic to provide a more accurate model of human opinions in the context of strategic decision-making, (see Chang et al. 2000; Jafari et al. 2008). The main advantage of the formation of such a group opinion is to make it more stable compared to the opinion of a single expert.