The aim of the present paper is to introduce and study the notions of ${\cal{RP}}_I$-sets, ${\cal{RPC}}_I$-sets and $\cal{RC}_I$-sets. Properties of ${\cal{RP}}_I$-sets, ${\cal{RPC}}_I$-sets and ${\cal{RC}}_I$-sets are investigated. Also, various decompositions in ideal spaces are established via generalized closedness with ${\cal{RP}}_I$-sets, ${\cal{RPC}}_I$-sets and ${\cal{RC}}_I$-sets.