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

Authors : Alexander V{S}OSTAK, Aleksandrs ELKİNS

Pages : 15-32

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Publication Date : 2017-02-01

Article Type : Research Paper

Abstract :We introduce a certain many-valued generalization of the concept of an $L$-valued equality called an $L^M$-valued equality. Properties of $L^M$-valued 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.
Keywords : L^M valued equalities, L^M rough approximation operators, ML graded ditopologies