On stability in possibilistic linear equality systems with Lipschitzian fuzzy numbers (Q910455)

Fuzzy numbers [cf. \textit{R. Goetschel} jun. and \textit{W. Voxman}, Fuzzy Sets Syst. 10, 87-99 (1983; Zbl 0521.54001)] with membership functions satisfying Lipschitz condition with a constant \(L>0\) are used as fuzzy coefficients in a system of linear equations. For any \(\delta >0\) it is proved that \(\delta\)-perturbations of fuzzy coefficients \(A_{i,k},B_ i: {\mathbb{R}}\to [0,1]\) for \(i=1,2,....,m\), \(k=1,2,...,n\) make \(L\delta\)- perturbation of the following fuzzy solution (\(\Sigma\) denotes n-ary addition of fuzzy numbers): \[ S(x_ 1,...,x_ n)=\min_{1\leq i\leq m}\sup_{t\in {\mathbb{R}}}\min ((\sum^{n}_{k=1}A_{i,k}x_ k)(t),\quad B_ i(t)). \] The paper simplifies a result of \textit{M. Kovács}, \textit{F. P. Vasil'ev} and the author [Mosc. Univ. Comput. Math. Cybern. 1989, No.1, 4-9 (1989); translation from Vestn. Mosk. Univ., Ser. XV 1989, No.1, 5-9 (1988; Zbl 0651.65028)].