Fuzzy　transfer　learning　has　the　potential　to　enhance　the　performance　of　a　task　in　the　target　scene　by　leveraging　knowledge　from　the　source　scene.　However,　the　existence　of　scene　discrepancies　between　the　two　scenes　poses　two　major　problems　for　fuzzy　transfer　learning:　1)　the　mismatch　between　the　distribution　of　source　knowledge　and　the　target　task,　and　2)　the　mismatch　between　the　learning　ability　of　the　target　task　and　the　source　knowledge.　To　address　these　challenges,　we　propose　a　fuzzy　transfer　learning　algorithm　called　Knowledge-Task　Matching　Fuzzy　Transfer　Learning　(KTM-FTL),　which　aims　to　adaptively　match　the　source　knowledge　and　the　target　task.　Firstly,　we　develop　a　knowledge　matching　mechanism　that　balances　matching　accuracy　and　diversity　to　reconstruct　the　knowledge　from　the　source　scene.　This　process　enables　the　source　knowledge　to　align　more　accurately　with　the　requirements　of　the　target　scene＇s　task.　Secondly,　we　design　a　task　matching　mechanism　that　allows　for　learning　the　source　knowledge　at　different　levels　of　granularity.　This　approach　enables　the　learning　ability　of　the　target　Feedforward　Neural　Network　(FNN)　to　match　the　complexity　of　the　source　knowledge,　thereby　improving　its　generalization　performance.　Thirdly,　we　conduct　theoretical　analysis　of　the　proposed　KTM-FTL,　including　an　examination　of　its　computational　complexity　and　error　bound.　These　analyses　provide　valuable　insights　for　the　successful　application　of　KTM-FTL.　Finally,　we　evaluate　the　performance　of　the　proposed　KTM-FTL　on　several　benchmark　problems　as　well　as　real-world　problems.　The　experimental　results　demonstrate　the　significant　improvements　achieved　by　KTM-FTL　when　compared　to　state-of-The-Art　algorithms.　©　2023　IEEE.