基于TFNCD算子的三角模糊數(shù)多屬性群決策

摘要： 針對屬性權(quán)重和專家權(quán)重全部未知的三角模糊數(shù)(triangular fuzzy number,TFN)多屬性群決策問題,在TFN熵的基礎(chǔ)上構(gòu)造了確信度指標(biāo)來量化對決策信息的信任程度,構(gòu)建了TFN確信度(TFN certitude degree,TFNCD)算子,并證明了其置換不變性、冪等性和有界性等性質(zhì),結(jié)合支持度確定專家權(quán)重,提出了基于TFNCD算子的屬性信息集結(jié)新方法。最后,通過算例的對比分析驗(yàn)證了TFNCD算子及其集結(jié)方法的有效性,該方法充分考慮了TFN類型的數(shù)據(jù)特征和兩種權(quán)重完全未知的情況,且屬性信息集結(jié)更加客觀高效,計(jì)算相對簡便,為TFN多屬性決策問題提供了新的信息集結(jié)方式和解決思路。
With regarding to the multi-attribute group decision-making problem of the triangular fuzzy number(TFN)with the attribute weights and experts weights being unknown,the confidence index is constructed based on the TFN entropy to quantify the degree of certitude to the decision information,and the TFN certitude degree(TFNCD)operator is introduced and its properties,such as the invariance of displacement transformation,the idempotence and the boundedness are proved.And the expert weights are determined combined with the degree of support.Finally,a method of attribute information aggregation is proposed,and the effectiveness of the TFNCD operator and the aggregated approach are verified by the empirical analysis.Moreover,the approach is built on the independence of experts,where the data features of the TFNs and the completely unknown weights of attributes and experts are fully considered,resulting in the objectivity and high efficiency in the information aggregation with relatively reduced computation.Therefore,it provides an information aggregation mode and solution to the multi-attribute group decision-making problem with TFN.