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This paper addresses the properties and structures of EI algebra and EI n algebra in the framework of Liu [Fuzzy Sets and Systems 95 (1998) 179]. The main contribution of the paper is that the expressions of both Ã-irreducible elements (or^-irreducible elements) in molecular lattice ðEM; PÞ, and ðEX 1 Á Á Á X n M; PÞ are developed, and that the standard minimal family of elements in molecular lattice ðEM; PÞ and ðEX 1 Á Á Á X n M; PÞ is formulated. It is proved that neither molecular lattice ðEM; PÞ nor molecular lattice ðEX 1 Á Á Á X n M; PÞ is a fuzzy lattice.

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