Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: These new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem, where the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares.
259 citations
TL;DR: The concepts of fuzzy continuity, product and quotient spaces are presented, and their fundamental properties are obtained in fuzzifying topology.
259 citations
TL;DR: Fuzzy set theory is established as a theoretical basis for ordination, and is employed in a sequence of examples in an analysis of forest vegetation of western Montana, U.S.A.
Abstract: Fuzzy set theory is an extension of classical set theory where elements of a set have grades of membership ranging from zero for non-membership to one for full membership. Exactly as for classical sets, there exist operators, relations, and mappings appropriate for these fuzzy sets. This paper presents the concepts of fuzzy sets, operations, relations, and mappings in an ecological context. Fuzzy set theory is then established as a theoretical basis for ordination, and is employed in a sequence of examples in an analysis of forest vegetation of western Montana, U.S.A. The example ordinations show how site characteristics can be analyzed for their effect on vegetation composition, and how different site factors can be synthesized into complex environmental factors using the calculus of fuzzy set theory. In contrast to current ordination methods, ordinations based on fuzzy set theory require the investigator to hypothesize an ecological relationship between vegetation and environment, or between different vegatation compositions, before constructing the ordination. The plotted ordination is then viewed as evidence to corroborate or discredit the hypothesis. I am grateful to Dr R. D. Pfister (formerly USDA Forest Service) for kind permission to publish data from a Forest Service study. I would like to gratefully acknowledge the helpful comments and criticisms of Drs. G. Cottam, J. D. Aber, T. F. H. Allen, E. W. Beals, I. C. Prentice, C. G. Lorimer, and two anonymous reviewers.
258 citations
TL;DR: A revised method is proposed which can avoid problems of Chu and Tsao's method for ranking fuzzy numbers, and it is easy to rank fuzzy numbers in a way similar to the original method.
Abstract: In 2002, Chu and Tsao proposed a method to rank fuzzy numbers. They employed an area between the centroid and original points to rank fuzzy numbers; however there were some problems with the ranking method. In this paper, we want to indicate these problems of Chu and Tsao's method, and then propose a revised method which can avoid these problems for ranking fuzzy numbers. Since the revised method is based on the Chu and Tsao's method, it is easy to rank fuzzy numbers in a way similar to the original method.
258 citations
10 Aug 1994
TL;DR: An introductory explanation about the approach is given, a lower bound of the minimal number of training samples is found, and it is shown that a minimum squared error criterion leads to the best approximate for the optimal Bayes classifier.
Abstract: This paper presents an attempt to characterize the performance of methods of classification based on fuzzy integral. After an introductory explanation about the approach, a lower bound of the minimal number of training samples is found, and it is shown that a minimum squared error criterion leads to the best approximate for the optimal Bayes classifier. Some tests on simulated and real data are provided.
257 citations