On modular inequalities of interval-valued fuzzy soft sets characterized by soft J-inclusions

Abstract

This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations of interval-valued fuzzy soft sets, we first investigate some basic properties of soft J-inclusions and soft L-inclusions. Then a new concept called upward directed interval-valued fuzzy soft sets is defined and some equivalent characterizations are presented. Furthermore, we consider modular laws in lattice theory and find that classical modular inequalities in lattice theory are not valid for interval-valued fuzzy soft sets. Finally, we present some interesting inequalities of interval-valued fuzzy soft sets by virtue of soft J-inclusions and related notions.