L M-valued equalities, L M-rough approximation operators and ML-graded ditopologies

We introduce a certain many-valued generalization of the concept of an L-valued equality called an L M-valued equality. Properties of L Mvalued equalities are studied and a construction of an L M-valued equality from a pseudo-metric is presented. L M-valued equalities are applied to introduce upper and lower L M-rough approximation operators, which are essentially many-valued generalizations of Z. Pawlak's rough approximation operators and of their fuzzy counterparts. We study properties of these operators and their mutual interrelations. In its turn, L M-rough approximation operators are used to induce topological-type structures, called here ML-graded ditopologies.

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