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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.

##### MSC:
 65G30 Interval and finite arithmetic 03E72 Theory of fuzzy sets, etc. 26E50 Fuzzy real analysis
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##### References:
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