Abstract
In this paper, we introduce the algebra Mnn(L) of square matrices over residuated lattice L. The operations are induced by the corresponding operations of L. It is shown that the defined algebra behaves like a residuated lattice, but there are some slight differences. The properties of this algebra with respect to special residuated lattices are investigated. The notions of filter and ideal together with their roles are specified.
Highlights
Matrix theory plays an important role in various areas of science and engineering to represent di¤erent types of binary relations
We introduced the algebra of square matrices over a commutative residuated lattice L and investigated some properties of this structure
We showed that this algebra behaves like a residuated lattice, but there are some di¤erences
Summary
Matrix theory plays an important role in various areas of science and engineering to represent di¤erent types of binary relations. Motivated by results of linear algebra over ...elds, rings and tropical semirings, Wilding presented a systematic way to understand the behavior of matrices with entries in an arbitrary semiring [14] He focuses on three closely related problems concerning the row and column spaces of matrices. The papers on matrices with entries in lattices (fuzzy, intuitionistic fuzzy, residuated) do not mention the algebraic structure of the collection of corresponding matrices. This highly motivates us to consider the set of all square matrices with entries in a residuated lattice. We end up with conclusion part in which our goal for the coming paper is given
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