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This paper considers the resolution of finite fuzzy relation equations with sup–inf composition over a bounded Brouwerian lattice. The solution sets of finite fuzzy relation equations on a bounded Brouwerian lattice are described in a similar way as those of linear spaces of n-dimensional vectors in linear algebra.
Up to now, how to solve a fuzzy relation equation in a complete Brouwerian lattice is still an open problem as Di Nola et al. point out. To this problem, the key problem is whether there exists a minimal element in the solution set when a fuzzy relation equation is solvable. In this paper, we first show that there is a minimal element in the solution set of a fuzzy relation equation A X=b (where...
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