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Fuzzy partitions and relations; an axiomatic basis for clustering. (English) Zbl 0442.68093


MSC:

68T10 Pattern recognition, speech recognition
62H30 Classification and discrimination; cluster analysis (statistical aspects)
03E20 Other classical set theory (including functions, relations, and set algebra)
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References:

[1] Zadeh, L. A., Similarity relations and fuzzy orderings, Inf. Sci., 3, 177-200 (1971) · Zbl 0218.02058
[2] Tamura, S.; Higuchi, S.; Tanaka, K., Pattern classification based on fuzzy relations, IEEE Trans. SMC, 61-66 (1971) · Zbl 0224.68012
[3] Kandel, A.; Yelowitz, L., Fuzzy chains, IEEE Trans. SMC, 61-66 (1971)
[4] Dunn, J., A graph theoretic analysis of pattern classification via Tamura’s fuzzy relation, IEEE Trans. SMC, 310-313 (1974) · Zbl 0297.68077
[5] Duda, R.; Hart, P., Pattern Classification and Scene Analysis (1973), Wiley-Interscience: Wiley-Interscience New York · Zbl 0277.68056
[6] Bezdek, J.; Harris, D., Convex decompositions of fuzzy partitions (in review), Inf. Sci. (1977)
[7] Rosenfeld, A., Fuzzy graphs, (Zadeh, L. A.; etal., Fuzzy Sets and their Applications to Cognitive and Decision Processes (1975), Academic Press: Academic Press New York), 77-96
[8] Yeh, R.; Bang, S., Fuzzy relations, fuzzy graphs, and their applications to clustering analysis, (Zadeh, L. A.; etal., Fuzzy Sets and Their Applications to Cognitive and Decision Processes (1975), Academic Press: Academic Press New York), 125-170
[9] Bezdek, J., Mathematical models for systematics and taxonomy, (Estabrock, G., Proc. Eighth Int. Conf. Numerical Taxonomy (1975), Freeman: Freeman SF), 143-166
[10] Crowson, R., Classification and Biology (1970), Atherton Press: Atherton Press New York
[11] Zadeh, L. A., Fuzzy sets, Inf. Cont., 338-353 (1965) · Zbl 0139.24606
[12] Ruspini, E., A new approach to clustering, Inf. Cont., 22-32 (1969) · Zbl 0192.57101
[13] Woodbury, M.; Clive, J., Clinical pure types as a fuzzy partition, J. Cybernetics, 111-121 (1974) · Zbl 0322.62071
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