Since A. Rosenfeld proposed the concept of fuzzy groups in 1971, fuzzy algebra forms a branch of fuzzy mathematics. The authors of this paper try to systematically study fuzzy subalgebras of a universal algebra, which is a kind of quite basic work including two parts of contents: one introduces some fundamental concepts such as \(T\)-fuzzy sets, \(LT\)-fuzzy sets, complete lattices \(LT\), \(FLT(U)\), \(CFLT(U)\) and \(DSTB(U)\) etc., and another is the main work with respect to fuzzy algebras, discussing plain semi-Post algebras (psP-algebra) of type \(T\) as axiomatic systems, and shows that the algebraic systems \((LT,U,\cap,\Rightarrow,\neg,(d_ t)_{t\in T},(e_ s)_{s\in LT})\), \(FLT(U)\), \(CFLT(U)\), and \(DSTB(U)\) are psP-algebra of type \(T\).