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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

Citations:

Zbl 0582.03040
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Full Text: DOI

References:

[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, (Thèse d’Etat (1983), Univ. de Grenoble: Univ. de Grenoble France) · Zbl 0546.94036
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic: 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: Masson Paris · Zbl 0674.68059
[7] Dubois, D.; Prade, H.; Testemale, C., Fuzzy pattern matching with extended capabilities: proximity notions, importance assessment, random sets, (Bandler, W.; Kandel, A., Recent Developments in the Theory and Applications of Fuzzy Sets. Recent Developments in the Theory and Applications of Fuzzy Sets, Proceedings of NAFIPS’ 86 (1986)), 125-139, New Orleans, La.
[8] Kandel, A.; Byatt, W. J., Fuzzy sets, fuzzy algebra and fuzzy statistics, (Proc. IEEE, 68 (1978)), 1619-1639
[9] Sugeno, M., Fuzzy measures and fuzzy integrals: A survey, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 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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