Abstract
In this paper the concept of twisted extended intersection soft ordered semi group or twisted extended intersection soft partially ordered semi group (briefly, TEISOsG or TEISPOsG), twisted restricted intersection soft ordered semi group or twisted restricted intersection soft partially ordered semi group (TRISOsG or TRISPOsG), twisted extended union soft ordered semi group or twisted extended union soft partially ordered semi group( TEUSOsG or TEUSPOsG ), twisted restricted union soft ordered semi group or twisted restricted union soft partially ordered semi group (TRUSOsG or TRUSPOsG), fully twisted extended union soft ordered semi group or fully twisted extended union soft partially ordered semi group (FTEUSOsG or FTEUSPOsG), fully twisted restricted union soft ordered semi group or fully twisted restricted union soft partially ordered semi group (FTRUSOsG or FTRUSPOsG), twisted soft ideal (TS-ideal), restricted twisted soft ideal(RTS-ideal), twisted soft interior ideal (TS-interior ideal), restricted twisted soft interior ideal (RTS-interior ideal), double twisted soft interior ideal (DTS-interior ideal), restricted double twisted soft interior ideal (RDRTS-interior ideal), strong double twisted soft interior ideal (St-DTS-interior ideal), restricted double twisted soft interior ideal (RSt-DRTS-interior ideal), are defined and some interesting results are proved. These concepts are also illustrated with the help of examples.