Although　the　Wang–Mendel　(WM)　method,　a　typical　way　of　fuzzy　modeling,　can　rapidly　obtain　fuzzy　rules　from　data　to　construct　fuzzy　systems　with　good　interpretability,　its　accuracy　is　not　high.　In　the　literatures,　many　optimization　approaches　are　proposed　to　improve　the　accuracy　of　the　WM　method,　but　the　optimization　process　is　in　general　time-consuming.　A　shallow　or　single　fuzzy　system　cannot　deal　with　“the　curse　of　dimensionality”,　which　makes　it　challenging　to　realize　modeling　of　high-dimensional　data.　Inspired　by　deep　neural　networks,　building　deep　fuzzy　systems　(DFS)　through　many　shallow　fuzzy　systems　will　become　a　new　direction　of　fuzzy　modeling　for　high-dimensional　data　modeling.　As　a　building　block　in　DFS,　each　shallow　fuzzy　system　should　have　the　characteristics　of　high　precision　and　fast　training　speed　to　ensure　the　operating　efficiency　of　DFS.　This　paper　proposes　a　Fast　Learning-algorithm　with　Optimized　Weights　for　Fuzzy　Systems　(FLOWFS)　in　the　following　three　steps:　(1)　Obtain　a　basic　fuzzy　system　with　full　rules　through　fast　training;　(2)　Assign　each　fuzzy　rule　a　weight　starting　with　1;　(3)　Develop　a　fast　learning-algorithm　optimal　weights　via　the　least　square　method　and　coefficient　regularization.　Aiming　at　the　regression　problems,　FLOWFS　is　compared　with　the　back　propagation　neural　network　(BP),　radial　basis　function　neural　network　(RBF),　the　WM　method　and　long　short-term　memory　(LSTM)　on　three　classic　datasets　of　UCI.　The　experimental　results　show　that:　(1)　FLOWFS　has　achieved　a　higher　prediction　accuracy;　(2)　Compared　with　the　WM　method,　FLOWFS　not　only　has　greater　accuracy,　but　also　is　faster　in　training;　(3)　In　terms　of　comprehensive　indicators　of　accuracy　and　running-time,　FLOWFS　has　the　best　performance.　Therefore,　FLOWFS　can　provide　good　fuzzy　building　blocks　for　DFS　to　enable　fast　modeling　of　high-dimensional　data　and　achieve　good　interpretability　and　high　accuracy.　©　2022,　The　Author(s)　under　exclusive　licence　to　Taiwan　Fuzzy　Systems　Association.