Fuzzy　analytic　hierarchy　process　(AHP)　proves　to　be　a　very　useful　methodology　for　multiple　criteria　decision-making　in　fuzzy　environments,　which　has　found　substantial　applications　in　recent　years.　The　vast　majority　of　the　applications　use　a　crisp　point　estimate　method　such　as　the　extent　analysis　or　the　fuzzy　preference　programming　(FPP)　based　nonlinear　method　for　fuzzy　AHP　priority　derivation.　The　extent　analysis　has　been　revealed　to　be　invalid　and　the　weights　derived　by　this　method　do　not　represent　the　relative　importance　of　decision　criteria　or　alternatives.　The　FPP-based　nonlinear　priority　method　also　turns　out　to　be　subject　to　significant　drawbacks,　one　of　which　is　that　it　may　produce　multiple,　even　conflict　priority　vectors　for　a　fuzzy　pairwise　comparison　matrix,　leading　to　entirely　different　conclusions.　To　address　these　drawbacks　and　provide　a　valid　yet　practical　priority　method　for　fuzzy　AHP,　this　paper　proposes　a　logarithmic　fuzzy　preference　programming　(LFPP)　based　methodology　for　fuzzy　AHP　priority　derivation,　which　formulates　the　priorities　of　a　fuzzy　pairwise　comparison　matrix　as　a　logarithmic　nonlinear　programming　and　derives　crisp　priorities　from　fuzzy　pairwise　comparison　matrices.　Numerical　examples　are　tested　to　show　the　advantages　of　the　proposed　methodology　and　its　potential　applications　in　fuzzy　AHP　decision-making.　(C)　2010　Elsevier　Inc.　All　rights　reserved.