The methodologies for fuzzy and stochastic multi-objective programming are compared. Considered is the following program: (1) \(\min z=CX\) \((k=1,2,\dots,K)\) subject to \(a_ iX\geq b_ i\) \((i=1,2,\dots,m)\), \(a_ iX=b_ i\) \((i=m+1,m+2,\dots,n)\), \(X\geq 0\), where \(c_ 1,c_ 2,\dots,c_ K\) and \(a_ i\), \(b_ i\) are vectors of fuzzy trapezoidal numbers. The discussion is concentrated on variants of (1) and their solutions. A stochastic linear program is formulated in the same format as (1) but the parameters \(C\), \(a_ i\), \(b_ i\) are viewed as random variables. Different methods from the literature are reviewed and compared. Finally some similarities in the approaches to fuzzy and stochastic programming in the context of the linear program (1) are revealed.