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Ovchinnikov, Sergei

Similarity relations, fuzzy partitions, and fuzzy orderings. (English) Zbl 0725.04003

Fuzzy Sets Syst. 40, No. 1, 107-126 (1991).
Fuzzy relations form a basic and important concept in fuzzy set theory, which was introduced by Zadeh in his very first paper on fuzzy sets. The author of the present paper discusses in detail fuzzy relations, especially fuzzy similarity relations. Then he studies fuzzy partitions and fuzzy orderings. The results on fuzzy orderings in this paper are interesting and they will have many fields of applications as fuzzy clustering, fuzzy decision-making, fuzzy games, and the fundamentals of fuzzy functions.
Reviewer: Li Hongxing (Beijing)

Cited in 1 Review
Cited in 59 Documents

MSC:

03E72 Theory of fuzzy sets, etc.

Keywords:

fuzzy preference relations; fuzzy set; fuzzy relations; fuzzy similarity relations; fuzzy partitions; fuzzy orderings
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\textit{S. Ovchinnikov}, Fuzzy Sets Syst. 40, No. 1, 107--126 (1991; Zbl 0725.04003)
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References:

[1] Baas, S. M.; Kwakernaak, H., Rating and ranking of multiple aspect alternatives using fuzzy sets, Automatica, 13, 47-58 (1977) · Zbl 0363.90010
[2] Bezdek, J. C.; Harris, J. D., Fuzzy partitions and relations: An axiomatic basis for clustering, Fuzzy Sets and Systems, 1, 111-127 (1978) · Zbl 0442.68093
[3] Bortolan, G.; Degani, R., A review of some methods for ranking fuzzy sets, Fuzzy Sets and Systems, 15, 1-19 (1985) · Zbl 0567.90056
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press · Zbl 0444.94049
[5] Dubois, D.; Prade, H., The use of fuzzy numbers in decision analysis, (Gupta, M.; Sanchez, E., Fuzzy Information and Decision Processes (1982), North-Holland: North-Holland Amsterdam) · Zbl 0571.04001
[6] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. Sci., 30, 183-224 (1983) · Zbl 0569.94031
[7] Birkhoff, G., (Lattice Theory, AMS, Vol. XXV (1979), American Mathematical Society: American Mathematical Society Providence, RI)
[8] Menger, K., Probabilistic theories of relations, (Proc. Nat. Acad. Sci. (Math.), 37 (1951)), 178-180 · Zbl 0042.37103
[9] Ovchinnikov, S., Structure of fuzzy binary relations, Fuzzy Sets and Systems, 6, 169-195 (1981) · Zbl 0464.04004
[10] Ovchinnikov, S.; Riera, T., On fuzzy classifications, (Yager, R., Fuzzy Set and Possibility Theory: Recent Developments (1982), Pergamon Press: Pergamon Press New York), 120-132
[11] Ovchinnikov, S., Transitive fuzzy orderings of fuzzy numbers, Fuzzy Sets and Systems, 30, 283-295 (1989) · Zbl 0675.06002
[12] Roberts, F. S., Measurement Theory (1979), Addison-Wesley: Addison-Wesley Reading, MA
[13] Roubens, M.; Vincke, P., Preference Modeling (1985), Springer-Verlag: Springer-Verlag Berlin
[15] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), North-Holland: North-Holland Amsterdam · Zbl 0546.60010
[16] Yeh, R. T.; Bang, S. Y., Fuzzy relations, fuzzy graphs, and their applications in clustering analysis, (Zadeh, L. A.; Fu, K. S.; Tanaka, K.; Shimura, M., Fuzzy Sets and Their Applications to Cognitive and Decision Processes (1975), Academic Press: Academic Press New York), 125-149
[17] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[18] Zadeh, L. A., Similarity relations and fuzzy orderings, Inform. Sci., 3, 177-200 (1971) · Zbl 0218.02058
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