Abstract| Uncertainty is present in virtually all replacement decisions due to unknown future events, such as revenue streams, maintenance costs, and in°ation. Fuzzy sets provide a mathematical framework for explicitly incorporating imprecision into the decision making model, especially when the system involves human subjectivity. This paper illustrates the use of fuzzy sets and possibility theory to explicitly model uncertainty in replacement decisions via fuzzy variables and fuzzy numbers. In particular, a fuzzy set approach to economic life of an asset calculation as well as a¯-nite horizon single asset replacement problem with multiple challengers is discussed. Because the use of triangular fuzzy numbers provides a compromise between computational efciency and realistic modeling of the uncertainty, this discussion emphasizes fuzzy numbers. The algorithms used to determine the optimal replacement policy incorporate fuzzy arithmetic, dynamic programming with fuzzy rewards, the vertex method, and various ranking methods for fuzzy numbers. A brief history of replacement analysis, current conventional techniques, the basic concepts of fuzzy sets and possibility theory, and the advantages of the fuzzy generalization are also discussed.
Defuzzification is a very important step in fuzzy systems applications. There are a number of different defuzzification methods reported in the literature. In this paper, the concept of defuzzification filters in a control system setting is first discussed and a methodology for designing such filters considered. As will be seen, the design of such filters requires the knowledge of the plant model and its inverse. A reference control signal is computed and then is used to generate the actual defuzzified control signal which will be applied to control the plant. The application of the defuzzification filter is made by introducing the filter into a power system in which a neuro-fuzzy self-learning controller was applied to stabilize the system but success could not always be guaranteed. With the defuzzification filter, however, the system is always stabilized. Simulation results are presented. ᮊ 2000 Academic Press
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