An investigation on algebraic structure of soft sets and soft filters over residuated lattices. (Q2014915)

Summary: We introduce the notion of soft filters in residuated lattices and investigate their basic properties. We investigate relations between soft residuated lattices and soft filter residuated lattices. The restricted and extended intersection (union), \(\vee\) and \(\wedge\)-intersection, Cartesian product, and restricted and extended difference of the family of soft filters residuated lattices are established. Also, we consider the set of all soft sets over a universe set \(U\) and the set of parameters \(P\) with respect to \(U\), \(\mathrm{Soft}_P(U)\), and we study its structure.