Computer based support of reasoning in the presence of fuzziness

摘要

Many important problems encountered in managerial decision making are unstructured, making them difficult to solve by preset algorithms. Much of the complexity of such problems is due to the reasoning that is needed to construct solution procedures for each problem instance. Thus, any Decision Support System (DSS) designed for such problems should support this reasoning activity, in addition to data access and computational activities. Yet, existing DSS generally do not provide much reasoning support. One of the difficulties faced in building automated systems to support such reasoning is that much of the knowledge typically available for unstructured problems is imprecise, where imprecision may be caused by either fuzziness, uncertainty, or both. In this paper, we address the problem of supporting problem solving with fuzzy knowledge. We develop a formal method for representing fuzzy knowledge, using a framework of mathematical logic. Using this method, fuzziness in all the major constructs needed to describe knowledge can be represented. Relationships can be constructed using fuzzy operators and terms, and components in relationships can be weighted by their relative significance. Also, computational procedures and data access procedures can be directly integrated into the reasoning process. Knowledge thus represented can be manipulated using suitable reasoning mechanisms. The fuzzy inference methods we present, enable the generation of acceptable solutions to problems even when some of the knowledge used is highly imprecise and/or incomplete. Other desirable features, such as explanation of solution procedures and user participation in problem solving, are also supported by our methodology. In addition, we develop bounding procedures, which convey the imprecision in the reasoning process, and also help to reduce the complexity of the search process by pruning poor solutions. Finally, we describe a prototype system which implements the methods developed in this paper. Using example problems processed by the system, we illustrate the versatility of these methods, and also highlight their major features and potential utility in practical applications.