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Solutions of algebraic equations involving generalized fuzzy numbers. (English) Zbl 0726.65048
A fuzzy number is treated here as a family of intervals \(A=([a_ L(t),a_ R(t)])_{t\in [0,1]}\) with continuous, piece-wise differentiable functions \(a_ L\) and \(a_ R\). Obviously \(a_ L\leq a_ R\), \(a_ L\) increases and \(a_ R\) decreases in [0,1] [cf. R. Goetschel, W. Voxman, Fuzzy Sets Syst. 18, 31-43 (1986; Zbl 0626.26014)]. The paper presents sufficient and necessary conditions for fuzzy numbers A and C such that the families of interval solutions of the equations \(A+X=C,\quad A-X=C,\quad A*X=C,\quad A/X=C\) form a fuzzy number X.

65G30 Interval and finite arithmetic
03E72 Theory of fuzzy sets, etc.
26E50 Fuzzy real analysis
Full Text: DOI
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