Alternative solutions to traditional approaches to risk analysis and decision making using fuzzy logic

摘要

Fuzzy set theory (FST) and Fuzzy logic (FL) are one of the main components of soft computing which is a collection of techniques to handle hard problems in which the application of traditional approaches fails. The father of FST and FL stated that the dominant aim of SC is to exploit the tolerance for imprecision and uncertainty to achieve tractability, robustness, and low solution cost. Since its establishment the theory of fuzzy sets and fuzzy logic became very popular and received much attention especiallyudduring the last decade being applied in many different fields. The wide use of fuzzy controllers in many massproduced products resulted in the increase of research in fuzzy set theory and fuzzy logic. In this thesis we use the techniques that are based on FL and FST for risk analysis and risk-based decision making. There are several reasons for using FL and FST. Fuzzy logic is a true extension of conventional logic: thus anything that was built using conventional design techniques can be built withudfuzzy logic. Another advantage is that it is close to humanudreasoning, and it is easy to understand for the users who doudnot have strong mathematical knowledge. A fuzzy system allows the user to use and to reason with words instead of crisp numbers. In addition, FL also offers a wide range of operators to perform efficient combinations of fuzzy predicates. In this thesis we propose alternative solutions to the existing approaches that use FL and FST for risk analysis and risk-based decision making. We investigated the current approaches, and we actually found that there exists only a small amount of researches that focus on risk analysis by using fuzzy logic. As far as we found, there are very few approaches that are generic and representative enough to be applied generally and to be used for complex problems. The existing approaches are very specific, targeting a particular area concentrating on specific types of risks. In this thesis we propose several different frameworks and algorithms based on FST and FL. First, we introduce two algorithms to rank the generalized fuzzyudnumbers. The main reason for developing a new ranking algorithm is that the existing ranking algorithms have some disadvantages that make them not suitable for risk assessment and decision making. We used our algorithms in risk-aware decision making related to the choice of alternatives. Second, we introduce a pessimistic approach to assess the impact of risk factors on the overall risk. The methods that use the fuzzy weighted average often give a lower result than the real risk especially in the case of a large amount of input variables. Furthermore, the traditional approaches of using fuzzy inference systems may give the same result for different cases depending on the choice of the defuzzification method. For the pessimistic approach we used our developed algorithms of ranking generalized fuzzy numbers. Next we propose the use of Fuzzy Bayesian Networks (FBNs) for risk assessment. While there is a considerable number of studies for Bayesian networks (BNs) for risk analysis and decision making, as far as we found there is not a study to make use of FBNs even though FBNs seem more appropriate and straightforward to use for risk analysis and risk assessment. In general, there is only a small amount of studies about FBNs, and not in many application fields. The last approach discussed in this thesis is the use of Fuzzy Cognitive Maps (FCMs) for risk analysis and decision making. We propose a new framework for group decision making in risk analysis using Extended FCMs. In addition we developed a new type of FCMs, Belief Degree Distributed FCMs, and we show its use for decision making.