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Weighted minimum and maximum operations in fuzzy set theory. (English) Zbl 0605.03021
This short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper [ibid. 36, 85-121 (1985; Zbl 0582.03040)] as medians, and corrects a misleading statement about it.

MSC:
03E72 Theory of fuzzy sets, etc.
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Keywords:
medians
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[1] Bellman, R.E.; Zadeh, L.A., Decision-making in a fuzzy environment, Management sci., 17, B141-B164, (1970) · Zbl 0224.90032
[2] Cayrol, M.; Farreny, H.; Prade, H., Fuzzy pattern matching, Kybernetes, 11, 103-116, (1982)
[3] Dubois, D., Modèles mathematiques de l’imprécis et de l’incertain, en vue d’applications aux techniques d’aide à la décision, () · Zbl 0546.94036
[4] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic New York · Zbl 0444.94049
[5] Dubois, D.; Prade, H., A review of fuzzy set aggregation connectives, Inform. sci., 36, 85-121, (1985) · Zbl 0582.03040
[6] Dubois, D.; Prade, H., Théorie des possibilités. application à la représentation des connaissances en informatique, (1985), Masson Paris · Zbl 0674.68059
[7] Dubois, D.; Prade, H.; Testemale, C., Fuzzy pattern matching with extended capabilities: proximity notions, importance assessment, random sets, (), 125-139, New Orleans, La.
[8] Kandel, A.; Byatt, W.J., Fuzzy sets, fuzzy algebra and fuzzy statistics, (), 1619-1639
[9] Sugeno, M., Fuzzy measures and fuzzy integrals: A survey, (), 89-102
[10] Thöle, U.; Zimmermann, H.-J.; Zysno, P., On the suitability of the minimum and product operators for the intersection of fuzzy sets, Fuzzy sets and systems, 2, 167-180, (1979) · Zbl 0408.94030
[11] Zadeh, L.A., Probability measures of fuzzy events, J. math. anal. appl., 23, 421-427, (1968) · Zbl 0174.49002
[12] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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