Molodtsov's soft set theory provides a general mathematical framework for dealing with uncertainty. This paper aims to put forward a new soft set-(M, N)-soft intersection set, which is a generalization of soft intersection sets. We introduce (M, N)-S I (implicative) filters of R 0 -algebras. Some characterizations of these kinds of filters are established. In particular, we discuss the properties of (M, N)-soft congruences in R 0 -algebras. It can lay a foundation for providing a new soft

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... aic tool in considering many problems that contain uncertainties.