Generalized random strongly nonlinear complementarity problems for random fuzzy mappings (Q2710045)

A class of complementarity problems for random fuzzy mappings is studied, algorithms for solving such problems are proposed and convergence of these algorithms is proved. Authors' results extend and improve upon previously existing results in the field as, for instance, those of \textit{S. S. Chang} and \textit{N. J. Huang} [Fuzzy Sets Syst. 55, 227-234 (1993; Zbl 0790.90076)]. Although, the authors do not explicitly say that, it is interesting to observe that their results can be also interpreted in the context of the metric space of upper semicontinuous, quasiconcave functions \(\mathbb{R}^n\to [0,1]\) which have bounded support. This is a metric space with the levelwise extended Hausdorff metric and the techniques presented in the paper under review can be ued for approaching optimization problems in this space, a question considered, for example, by \textit{D. Diamond} and \textit{P. Kloeden} [Metric Spaces of Fuzzy Sets, World Scientific (1994; Zbl 0873.54019)] and, subsequently, by the reviewer [Libertas Math. 17, 1-7 (1997; Zbl 0961.90133)].