In　this　paper,　a　class　of　1-dimensional　fuzzy　numbers　is　studied.　The　definitions　of　arithmetic　operations　such　as　addition,　subtraction,　scalar　multiplication　and　multiplication　between　fuzzy　number　and　fuzzy　number　are　given　without　the　aid　of　a-level　set.　And　also　we　study　the　expectation,　variance,　covariance　of　fuzzy　random　variables　and　differential,　Stieltjes　integral　of　fuzzy　number-valued　functions　without　the　aid　of　set-valued　theory　which　is　very　different　from　the　present　research　approach.　Fuzzy　number-valued　Brownian　motion　and　its　properties　are　studied,　which　are　very　similar　to　real-valued　Brownian　motion.　©　2007　IEEE.