On AFS algebra—Part I.

This paper addresses the properties and structures of EI algebra and EIn 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 *-irreducible elements (or A-irreducible elements) in molecular lattice (EM, ≥), and (EX1 ··· XnM, ≥) are developed, and that the standard minimal family of elements in molecular lattice (EM, ≥) and (EX1 ··· XnM, ≥) is formulated. It is proved that neither molecular lattice (EM, ≥) nor molecular lattice (EX1 ··· XnM, ≥) is a fuzzy lattice. [ABSTRACT FROM AUTHOR]