—Data　fusion　in　the　Internet　of　Things　(IoT)　is　based　on　the　intersection　and　union　problems　of　sets　without　complete　set　restrictions　to　achieve　accurate　and　reliable　location　services.　However,　protecting　users’　privacy　in　IoT　is　challenging,　for　which　a　solution　is　proposed　herein　in　conjunction　with　secure　multiparty　computation　(MPC).　Using　the　proposed　solutions,　users’　privacy　can　be　ensured　while　achieving　accurate　and　reliable　location　positioning.　Current　privacy-preserving　schemes　used　for　data　fusion　require　a　set’s　elements　belonging　to　an　appropriate　complete　set,　and　the　range　of　elements　used　by　such　schemes　is　usually　integers.　Moreover,　a　unified　range　of　all　elements　in　a　set　cannot　be　determined　in　real　time　for　practical　scenarios.　Limiting　the　range　of　elements　to　integers　is　also　impossible,　because　the　type　of　data　collected　by　IoT　devices　is　uncertain.　To　address　these　issues,　new　encoding　and　transformation　methods　are　proposed　herein　to　map　a　set　of　rational　numbers　to　the　Cartesian　coordinate　system.　The　NTRU　encryption　scheme　is　used　to　design　the　intersection　and　union　MPC　protocols　of　rational　numbers’　sets　without　any　complete　set　restriction　under　the　semi-honest　model.　Then,　to　prevent　possible　malicious　behaviors　in　the　semi-honest　model　protocols,　MPC　protocols　for　the　intersection　and　union　of　rational　numbers’　sets　are　designed　without　any　complete　set.　The　security　of　the　protocols　is　demonstrated　by　applying　the　real/ideal　model　paradigm.　The　comparison　of　the　proposed　protocols　with　other　schemes　shows　that　our　protocols　have　higher　computational　efficiency.　©　2024　IEEE.　Personal　use　is　permitted,　but　republication/redistribution　requires　IEEE　permission.