Fuzzy　systems　(FSs)　are　popular　and　interpretable　machine　learning　methods,　represented　by　the　adaptive　neuro-fuzzy　inference　system　(ANFIS).　However,　they　have　difficulty　dealing　with　high-dimensional　data　due　to　the　curse　of　dimensionality.　To　effectively　handle　high-dimensional　data　and　ensure　optimal　performance,　this　paper　presents　a　deep　neural　fuzzy　system　(DNFS)　based　on　the　subtractive　clustering-based　ANFIS　(SC-ANFIS).　Inspired　by　deep　learning,　the　SC-ANFIS　is　proposed　and　adopted　as　a　submodule　to　construct　the　DNFS　in　a　bottom-up　way.　Through　the　ensemble　learning　and　hierarchical　learning　of　submodules,　DNFS　can　not　only　achieve　faster　convergence,　but　also　complete　the　computation　in　a　reasonable　time　with　high　accuracy　and　interpretability.　By　adjusting　the　deep　structure　and　the　parameters　of　the　DNFS,　the　performance　can　be　improved　further.　This　paper　also　performed　a　profound　study　of　the　structure　and　the　combination　of　the　submodule　inputs　for　the　DNFS.　Experimental　results　on　five　regression　datasets　with　various　dimensionality　demonstrated　that　the　proposed　DNFS　can　not　only　solve　the　curse　of　dimensionality,　but　also　achieve　higher　accuracy,　less　complexity,　and　better　interpretability　than　previous　FSs.　The　superiority　of　the　DNFS　is　also　validated　over　other　recent　algorithms　especially　when　the　dimensionality　of　the　data　is　higher.　Furthermore,　the　DNFS　built　with　five　inputs　for　each　submodule　and　two　inputs　shared　between　adjacent　submodules　had　the　best　performance.　The　performance　of　the　DNFS　can　be　improved　by　distributing　the　features　with　high　correlation　with　the　output　to　each　submodule.　Given　the　results　of　the　current　study,　it　is　expected　that　the　DNFS　will　be　used　to　solve　general　high-dimensional　regression　problems　efficiently　with　high　accuracy　and　better　interpretability.