Abstract
Fuzzy relation matrices are considered and the well-known Szpilrajn theorem on orderings is generalized to fuzzy orderings. Zadeh has already shown a generalized theorem, but another generalization is given in matrix form. Some interesting operations on fuzzy matrices are introduced, and their properties are mentioned briefly. The theorem is represented in terms of the matrix operations. The operations have many properties and are useful in the various applications of fuzzy matrices or fuzzy relations.
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