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This paper investigates the problem of solving sup-conjunctor composite finite interval-valued fuzzy relational equations over complete Brouwerian lattices. First, we introduce the notions of tolerable solution set, united solution set and controllable solution set, respectively and discuss their properties. Secondly, we obtain some necessary and sufficient conditions that these solution sets are...
This paper investigates the dimensions of ℒ-semilinear subspaces of Vn. It first obtains some necessary and sufficient conditions that each basis has the same number of elements. Then it presents that over some zerosumfree semirings, each basis also has the same number of elements. In the end, it discusses the relationships between the direct sums and the dimensions of semilinear subspaces of n-dimensional...
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