Soft set theory applied to residuated multilattices

Abstract

Dealing with uncertainty, imprecision and fuzziness, Soft set theory is one of many mathematical tools; it is a classical generalization of fuzzy set theory. Many researchers study the case of a universe set endowed with an algebraic structure. This paper uses residuated multilattices as the universe set for soft set theory. The notions of $f$-soft residuated multilattice, $r$-soft residuated multilattice, soft filter, filteristic residuated multilattice are defined, and several related properties are investigated.