不完整格的格序化
Lattice Ordering of Incomplete Lattice
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摘要: 研究了格序决策理论中格序结构不完整的问题.通过定义格上关键元及最小决定集的确定规则,得到了 一种直接由偏序集求最小完备格的并、交不可约元(关键元)的方法;从分析最小格的结构着手,应用逆序嵌入 映射的方法确定2个不存在最小(最大)上(下)确界的元素的最小(最大)上(下)确界,从而使得不完整格格序 化.最后,举例说明了该方法的可行性.Abstract: 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.
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Key words:
- lattice order decision-making /
- partial order /
- lattice /
- irreducible elements
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