Fuzzy　systems　are　widely　used　for　solving　complex　and　non-linear　problems　that　cannot　be　addressed　using　precise　mathematical　models.　Their　performance,　however,　is　critically　affected　by　how　they　are　constructed　as　well　as　their　fuzzy　rule　base.　Inspired　by　neural　networks　that　apply　a　multi-layer　structure　to　improve　their　performance,　we　propose　a　multi-layer　fuzzy　model　with　modified　fuzzy　rules　to　improve　the　approximation　ability　of　fuzzy　systems　without　losing　efficiency.　In　practical　applications,　the　fuzzy　rule　base　extracted　from　numerical　data　is　often　incomplete,　which　makes　a　fuzzy　system　less　robust.　To　address　this　problem,　a　non-linear　function　is　used　as　the　consequent　of　each　fuzzy　rule　based　on　fuzzy-rule　clustering　to　enhance　the　approximation　ability　of　the　fuzzy　rule　base.　In　addition,　exact　matching　of　fuzzy　rules　is　employed　based　on　the　fuzzy　rule＇s　antecedent　for　prediction.　By　doing　so,　only　one　rule　will　be　triggered　in　each　layer,　which　is　very　efficient.　Experimental　results　from　two　simulated　functions　and　three　practical　applications　confirm　that　our　proposed　multi-layer　fuzzy　model　can　outperform　other　well-established　fuzzy　models　in　terms　of　accuracy　and　robustness　without　sacrificing　efficiency.　©　2020　Elsevier　B.V.