Constructing fuzzy measures: a new method and its application to cluster analysis

Author

Yuan, Bo ; Klir, George J.

Author_Institution

Dept. of Syst. Sci. & Ind. Eng., State Univ. of New York, Binghamton, NY, USA

fYear

1996

fDate

19-22 Jun 1996

Firstpage

567

Lastpage

571

Abstract

We first prove that for a given set of data there exists a fuzzy measure fitting exactly the data if and only if there exists an exact solution of the associated fuzzy relation equation. Secondly, we continue to study the special neural network we proposed in Proc. IFSA´95 World Congress, pp. 61-64 (1995), and describe a learning algorithm for obtaining an approximate fuzzy measure when no one exactly fits the data. Finally, we propose a clustering method based on fuzzy measures and integrals. A benchmark data set, the well-known Iris data set, is adopted to illustrate the method

Keywords

data analysis; fuzzy set theory; learning (artificial intelligence); neural nets; pattern recognition; Iris data set; approximate fuzzy measure; benchmark data set; cluster analysis; data fitting; fuzzy integrals; fuzzy measures construction; fuzzy relation equation; learning algorithm; neural network; nonadditive measures; Clustering algorithms; Fitting; Fuzzy neural networks; Fuzzy sets; Fuzzy systems; Industrial engineering; Integral equations; Intelligent systems; Neural networks; Power measurement;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Information Processing Society, 1996. NAFIPS., 1996 Biennial Conference of the North American

Conference_Location

Berkeley, CA

Print_ISBN

0-7803-3225-3

Type

conf

DOI

10.1109/NAFIPS.1996.534798

Filename

534798