Lattice Ordering of Incomplete Lattice

A problem in the lattice orderdecision-making theory,i. e., the structure of lattice order is incomplete, was investigated. By defining the regulation ofdetermining key elements and theminimal decision se,t a method was given to directly work out join-and meet-irreducible elements of the smallest complete lattice from a partial order se.t The inverse order embeddingmappingmethod was used to determine the greatest lowerbound or the leastupperbound of two elementswithoutthe greatest lowerbound or the least upper bound to obtain the lattice order of incomplete lattice. Finally, an examplewas given to illustrate the feasibility of thismethod.