Fuzzy Set Theory - and Its Applications
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Cites background or methods from "Fuzzy Set Theory - and Its Applicat..."
...In the following, we brie y review some basic definitions of fuzzy sets from [2, 11, 12, 14–16]....
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...ñ is a non-empty bounded closed interval contained in X and it can be denoted by ñ = [n l; n u]; n l and n u are the lower and upper bounds of the closed interval, respectively [11, 16]....
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Additional excerpts
...Most of the basic problems of FLC have been resolved, and researchers are now investigating advanced topics such as stability, adaptive fuzzy control, hybrid systems, neuro-fuzzy systems, and FLC systems tuned by genetic algorithms (GAs) that are inherently adaptive systems. Progress is fast in these areas, and promising experimental results have been obtained. With the rising popularity of FLC, more engineers will be trained in this area in the future. This training will lead to more applications of FLC systems and to rising field experience of the involved engineers. Fuzzy logic control is an integral part of modem control theory, not replacing conventional methods but rather complementing them. Since the literature in fuzzy control is too vast to be discussed in its entirety in this textbook, a summary is given below. It is primarily intended for those who have an extended interest in this area: One of the first books on fuzzy logic control was written by W. Pedrycz in 1989 [Pedrycz 1989] and focuses on many concepts of FLC. The use of fuzzy relations in connection with FLC systems is discussed thoroughly. A second edition of this popular book appeared in 1993 [Pedrycz 1993] and covers also new directions, such as neural network methods. Many survey articles on FLC have appeared in control journals in the last years, and we very much recommend the survey of Lee [1990], which covers all basic aspects....
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...The area of operations research will be considered as an example of a more application-oriented discipline, which is here called "technology," in which modeling plays a predominant role. Even though one might dispute whether operations research is a science or a technology, this discussion will follow Symonds, who, as the President of the Institute of Management Science, stated, "Operations Research is the development of general scientific knowledge" [Symonds 1965, p. 38511. What, now, is a model in operations research? Most authors using the term model take it for granted that the reader knows what a model is and what it means. Arrow, for instance, uses the term model as a specific part of a theory when he says, "Thus the model of rational choice as built up from pairwise comparisons does not seem to suit well the case of rational behaviour in the described game situation" [Arrow 19511. He presumably refers to the model of rational choice, because the theory he has in mind does not give a very adequate description of the phenomena with which it is concerned, but only provides a highly simplified schema. In the social and behavioral sciences as well as in the technologies, it is very common that a certain theory is stated in rather broad and general terms while models, which are sometimes required to perform experiments in order to test the theory, have to be more specific than the theories themselves. "In the language of logicians it would be more appropriate to say that rather than constructing a model they are interested in constructing a quantitative theory to match the intuitive ideas of the original theory" [Suppes 1961]. Rivett, in his book Principles of Model Building [1972], offers three different kinds of classifications of models; when enumerating the models that he suggests be put into the different classes, he no longer uses the term model but talks of "problems in this area" and "the theory of this area" as a not-too-well-defined entity of knowledge....
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