To　illustrate　data　uncertainty,　intuitionistic　fuzzy　sets　simply　use　membership　and　non-membership　degrees.　However,　in　some　cases,　a　more　complex　strategy　is　required　to　deal　with　imprecise　data.　One　of　these　techniques　is　generalized　intuitionistic　fuzzy　sets　(GIFSs),　which　provide　a　comprehensive　framework　by　adding　extra　factors　that　provide　a　more　realistic　explanation　for　uncertainty.　GIFSs　contain　generalized　membership,　non-membership,　and　hesitation　degrees　for　establishing　symmetry　around　a　reference　point.　In　this　paper,　we　applied　a　generalized　intuitionistic　fuzzy　set　approach　to　investigate　ambiguity　in　the　parameter　of　the　Lomax　life　distribution,　seeking　a　more　symmetric　assessment　of　the　reliability　measurements.　Several　reliability　measurements　and　associated　cut　sets　for　a　novel　L-R　type　fuzzy　sets　are　derived　after　establishing　the　scale　parameter　as　a　generalized　intuitionistic　fuzzy　number.　Additionally,　the　study　includes　a　range　of　reliability　measurements,　such　as　odds,　hazards,　reliability　functions,　etc.,　that　are　designed　for　the　Lomax　distribution　within　the　framework　of　generalized　intuitionistic　fuzzy　sets.　These　reliability　measurements　are　an　essential　tool　for　evaluating　the　reliability　characteristics　of　various　types　of　complex　systems.　For　the　purpose　of　interpretation　and　application,　the　results　are　visually　displayed　and　compared　across　different　cut　set　values　using　a　numerical　example.