Although　fuzzy　system　(FS)　is　highly　interpretable,　it　is　difficult　to　address　high-dimensional　big　data　due　to　the　curse　of　dimensionality.　On　the　contrary,　deep　neural　network　(DNN),　a　fashion　deep　learning　algorithm,　can　deal　with　high-dimensional　big　data　with　shortcomings　of　complex　model,　huge　calculation,　and　poor　interpretability.　We　present　a　model　of　random　locally　optimized　deep　fuzzy　system　(RLODFS)　and　four　specific　heuristic　implementation　algorithms,　which　combines　the　advantages　of　high　interpretability　of　FS　and　great　ability　of　processing　high-dimensional　big　data　of　DNN.　This　method　takes　Wang-Mendel　(WM)　algorithm　as　the　basic　module,　to　construct　a　RLODFS　by　bottom-up　parallel　structure.　Through　hierarchical,　random　group　and　combination-based　learning,　and　input　sharing,　it　can　retain　the　interpretability　and　dramatically　improve　the　computational　efficiency.　The　input　variables　of　the　low-dimensional　FS　are　randomly　grouped　by　isometric　sampling.　Four　implementation　algorithms　of　RLODFS　based　on　random　local　search　for　optimal　combination,　group　learning,　and　deep　structure　with　0,　1,　2,　and　3　input　sharing,　respectively,　named　as　RLODFS-S0,　RLODFS-S1,　RLODFS-S2,　and　RLODFS-S3,　are　developed　for　regression-oriented　problems.　Using　local　loops　to　find　the　best　combination　of　parameters,　our　final　algorithms,　RLODFS,　can　achieve　fast　convergence　in　training　phase,　and　also　superior　generalization　performance　in　testing.　Compared　with　six　classic　algorithms　in　12　datasets,　the　proposed　RLODFS　algorithms　are　not　only　highly　interpretable　with　just　some　fuzzy　rules　but　also　can　achieve　higher　precision,　less　complexity,　and　better　generalization.　Furthermore,　it　can　be　used　for　training　fuzzy　systems　on　datasets　of　any　size,　particularly　for　big　datasets.　Relatively,　RLODFS-S3　and　RLODFS-S2　achieve　the　best　in　comprehensive　performance.　More　importantly,　the　proposed　RLODFS　is　a　new　promising　method　of　deep　learning　with　good　interpretability　and　high　accuracy.