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Equations with fuzzy numbers. (English) Zbl 0664.04006
By Zadeh’s extension principle a binary operation * on the real numbers \({\mathbb{R}}\) is extended to fuzzy numbers \(f_ i: {\mathbb{R}}\to [0,1]\), \(i=1,2\), as follows \((f_ 1*f_ 2)(z)=\bigvee \{f_ 1(x_ 1)\wedge f_ 2(x_ 2):\) \(x_ 1*x_ 2=z\}\). Then the equation \(f*x=g\) is considered. Among other things the author investigates which conditions have to be verified by the cuts of f and g in order that this equation has a solution. For details we have to refer to the paper.
Reviewer: J.Albrycht

03E99 Set theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI
[1] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic · Zbl 0444.94049
[2] Goetschel, R.; Woxman, W., Topological properties of fuzzy numbers, Fuzzy sets and systems, 10, 87-99, (1983) · Zbl 0521.54001
[3] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic, (1980), Van Nostrand
[4] Mizumoto, M.; Tanaka, K., Some properties of fuzzy numbers, () · Zbl 0334.94020
[5] Nguyen, H.T., A note on the extension principle for fuzzy sets, J. math. anal. appl., 64, 369-380, (1978) · Zbl 0377.04004
[6] Sanchez, E., Solutions of fuzzy equations with extended operations, Fuzzy sets and systems, 12, 237-248, (1984) · Zbl 0556.04001
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