基于改進(jìn)Gini-Simpson指數(shù)的指標(biāo)及權(quán)重均為混合屬性的廣義灰靶決策方法

摘要： 提出了一種新的以改進(jìn)的Gini-Simpson指數(shù)為決策依據(jù)的指標(biāo)及權(quán)重均為混合屬性值的廣義灰靶決策方法。該方法構(gòu)造權(quán)重函數(shù)將不確定性混合指標(biāo)權(quán)重確定化,并以改進(jìn)的綜合加權(quán)Gini-Simpson指數(shù)作為方案決策的依據(jù)。首先將各方案的混合屬性指標(biāo)值轉(zhuǎn)化為二元聯(lián)系數(shù),并分解為確定項(xiàng)和不確定項(xiàng)以組成(確定,不確定)二元組數(shù);其次,分別獲得各屬性下靶心指標(biāo)的(確定,不確定)二元組數(shù);然后,構(gòu)造權(quán)重函數(shù)將不確定性權(quán)重確定化,繼而求得各方案的綜合加權(quán)Gini-Simpson指數(shù);最后以綜合加權(quán)的Gini-Simpson指數(shù)為依據(jù)對(duì)各方案進(jìn)行決策,以其值越小方案越優(yōu)。案例分析的結(jié)果驗(yàn)證了該法的可行性。
A novel improved Gini-Simpson index based generalised grey target decision method with index and weight both containing mixed attribute values is proposed.This method builds the weight function to transform the mixed attribute-based weights into the certain number-based weights and takes the improved comprehensive weighted Gini-Simpson indices to rank the alternatives.This method first transforms all alternatives' indices into binary connection numbers and divides them into the deterministic terms and uncertain terms to compose the two-tuple(determinacy,uncertainty)numbers.Then the target centre indices of two-tuple(determinacy,uncertainty)number are determined.Next the certain numberbased weights can be determined by the weight function.Following this,the comprehensive weighted GiniSimpson index of all alternatives can be obtained.Finally,the alternatives ranking is easy to be made with the Gini-Simpson index the smaller the better.A case study illustrates the proposed approach.