This　study　investigates　the　convergence　speed　and　mean　square　error　capability　of　the　Least　Mean　Square　(LMS)　adaptive　filtering　algorithm,　presenting　a　novel　approach　termed　the　Fuzzy　Variable　Learning　Rate　LMS　algorithm　based　on　convex　combination.　Firstly,　in　order　to　enhancing　convergence　speed,　an　enhanced　LMS　algorithm　employing　variable　learning　rate　based　on　sine　functions,　denoted　as　the　Improved　Variable　Step　Size　LMS　Algorithm　based　on　Sine　Function　(γ-SLMS),　is　introduced.　Building　upon　this,　to　mitigate　the　steady-state　error,　the　Fuzzy　Variable　Learning　Rate　LMS　Algorithm　based　on　Mamdani　Model　(FMS-LMS)　is　proposed.　Finally,　utilizing　a　convex　combination　framework,　the　Fuzzy　Variable　Learning　Rate　LMS　Adaptive　Filtering　Algorithm　Based　on　Convex　Combination　(cFMS-LMS)　is　formulated.　Simulation　results　indicate　that　the　cFMS-LMS　algorithm　surpasses　traditional　LMS　algorithms　in　both　convergence　speed　and　mean　square　error.　Furthermore,　it　shows　lower　computational　complexity　compared　to　LMS　algorithms　utilizing　Sugeno　fuzzy　inference.　©　2024　IEEE.