This　article　proposes　a　novel　online　and　self-learning　algorithm　to　the　identification　of　fuzzy　neural　networks,　which　not　only　learns　the　structure　and　parameters　online,　but　also　learns　the　threshold　parameters　by　itself　and　automatically.　For　structure　learning,　a　self-constructing　approach　including　adding　neurons　and　merging　highly　similar　fuzzy　rules　is　proposed　based　on　the　criteria　of　the　system　error　between　actual　and　model　output　and　the　maximum　firing　strength　of　neurons.　In　order　to　achieve　the　efficient　merging　computing,　a　new　calculation　method　of　similarity　degree　between　fuzzy　rules　is　developed.　Further　and　more　importantly,　the　varying　width　of　Gaussian　membership　functions　can　be　learned　by　itself　according　to　the　underfitting　and　overfitting　criteria.　Similarly,　different　from　the　existing　constant　threshold　of　similarity　degree　for　merging,　the　varying　threshold　of　similarity　degree　can　be　self-learned　according　to　the　real-time　accuracy　of　model.　The　proposed　self-learning　mechanism　significantly　improves　the　model　accuracy　and　greatly　enhances　the　easy　usability.　Several　benchmark　examples　are　implemented　to　illustrate　the　effectiveness　and　feasible　of　the　proposed　approach.