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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.
This paper deals with invertible matrices and semilinear spaces over commutative semirings. Some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained. The condition under which the cardinality of each basis of semilinear space of n-dimensional vectors is n is given. In the end, the factor rank of matrices over semirings is investigated.
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