Approach of Fuzzy Multi-objective Decision-Making Based on Lattice-Order Preference
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摘要: 运用格论,将方案优选的全序刻画拓展为格序刻画.基于决策理论和模糊集理论,提出了模糊多目标格序决策的概念,建立了模糊多目标格序决策模型.基于正、负理想解的概念,提出了该模型的2种算法.算法1是先对模糊指标值进行加权,然后确定模糊正、负理想解,通过比较每个方案与两者之间的差异选择满意解.算法2是直接在原模糊指标值的基础上确定模糊正、负理想解,并引入满意度的概念刻画每个方案与两者之间的差异,最后通过加权得到满意解.算法1较简单,算法2则能始终保持模糊元素的线性性质.算例表明,2种算法结果一致.Abstract: By using the lattice theory,the totally ordering description of scheme optimization was extended to the lattice ordering one.Based on the decision-making theory and the fuzzy set theory,the concept of fuzzy multi-objective lattice-order decision-making was put forward.By introducing the concepts of fuzzy positive and negative ideal solutions,a model for fuzzy multi-objective lattice-order decision-making was constructed,and two algorithms,algorithms 1and 2,for this model were proposed.With the algorithm 1,fuzzy indexes are weighted,then fuzzy positive and negative ideal solutions are determined,and finally a satisfying solution can be obtained by comparing the difference between each scheme and the two ideal solutions.With the algorithm 2,fuzzy positive and negative ideal solutions are determined directly based on fuzzy indexes,then the difference between each scheme and the two ideal solutions is described by introducing the concept of satisfactory degree,finally a satisfying solution can be obtained through weighting.A numerical example shows the consistency of satisfying solutions obtained using the two algorithms.
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