Exploring Digital Design

Abstract

In 1965 L.A. Zadeh presented a fuzzy set. After then, fuzzy clustering method was proposed in early stage. L.A. Zadeh presented the concept of similarity for a fuzzy set in 1981. Ruspini proposed a clustering method based on fuzzy decomposition. Dunn and Bezdek wrote a clustering based on IDODATA algorithm in terms of fuzzy concept. Many methods for fuzzy multivariate analysis were presented. For example, there are several approaches to multivariant analysis such as dynamic programming, M. Sugeno's measure, similarity concepts and clustering. M. Roubens and M.P. Windham discussed about the validity of clustering. Regarding hierarchical clustering, N. Osumi et al discussed it using fuzzy concepts. J. Watada et al proposed a heuristic hierarchical clustering which is employing similarity concepts of L.A. Zadeh's. There are many papers which discuss fuzzy clustering. In 1979 H. Tanaka et al proposed fuzzy linear regression model. This development broke through fuzzy multivariate analysis because no methods are proposed except clustering and hierarchical clustering till then. There are also various applications of fuzzy multicariant analyses. Furthermore, various data analyses were proposed based on the fuzzy linear regression model. For example, J. Watada et al developed Fuzzy time-series analysis and I. Hayashi developed GMDH method. This paper summarizes the 40 year history of Fuzzy Multivariate Methods. ©Springer-Verlag Berlin Heidelberg 2005.