Generalized Grey Target Decision Method for Mixed Attributes Based on Kullback-Leibler Distance

Abstract

A novel generalized grey target decision method for mixed attributes based on Kullback-Leibler (K-L) distance is proposed. The proposed approach involves the following steps: first, all indices are converted into index binary connection number vectors; second, the two-tuple (determinacy, uncertainty) numbers originated from index binary connection number vectors are obtained; third, the positive and negative target centers of two-tuple (determinacy, uncertainty) numbers are calculated; then the K-L distances of all alternatives to their positive and negative target centers are integrated by the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method; the final decision is based on the integrated value on a bigger the better basis. A case study exemplifies the proposed approach.

A novel generalized grey target decision method with index and weight both containing mixed types of data

“…Let D ¼ ððx 1 ; y 1 Þ; ðx 2 ; y 2 Þ; ...; ðx j ; y j Þ; ...; ðx m ; y m ÞÞ Τ and E ¼ ððp 1 ; q 1 Þ; ðp 2 ;q 2 Þ ; :::; ðp j ; q j Þ; ...; ðp m ; q m ÞÞ T be two vectors of two-tuple (determinacy, uncertainty) numbers with x j ; y j ; p j ; q j ≥ 0. And the weight vector W ¼ ðw 1 ; w 2 ;...; w m Þ T is given with which satisfying P m j¼1 w j ¼ 1, where A novel generalized grey target decision method w j > 0, j 5 1, 2,...,m. Then the CWKLD H W ðD; EÞ can be calculated using the following equation (Ma, 2018a):…”

“…Later, the equivalent method including cobweb area and incidence coefficient is proposed (Guan et al, 2015;Zeng et al, 2013). Besides, some other methods that proximity Kullback-Leibler (K-L) distance (Ma, 2018a) and Gini-Simpson (G-S) index (Ma, 2019a) are also presented, which is called mixed attribute generalized grey target decision method (GGTDM) . The GGTDM obeys the principle of the conventional GTDM, but its calculation process differs from the conventional one Ma, 2014Ma, , 2018b.…”

Kullback-Leibler Distance Based Generalized Grey Target Decision Method With Index and Weight Both Containing Mixed Attribute Values

“…The decision-making basis (DMB) of grey target decision method (GTDM) is referred to as the target center distance (TCD), which is the distance of each alternative and its target center. In certain number-based GTDM, Euclidean distance and Mahalanobis distance are often applied to obtain the TCDs [1], [2].However, the mixed attribute-based GTDM obtains the TCD in different ways: at first, the conventional Euclidean distance-based method was reported [3][4][5].Then the equivalent methods including cobweb area and correlation coefficient appeared [6], [7].Besides, the proximity-based method, entropy-based method and Gini-Simpson indexbased method were also investigated, as is named as generalized grey target decision method(GGTDM) [8][9][10]. The GGTDM differs from the conventional one in the calculation process, but obeys the same principle(e.g., [8], [9], [11][12][13]).…”

Extended Research on Grey Target Decisions for a Variable Target Centre Based on Decision Maker Preferences

“…Furthermore, other theories and methods have adapted the GTDM [14][15][16][17][18]. Ma and Ji proposed a generalised grey target decision method (GGTDM) [8,19], and a mixed-attribute GGTDM was developed based on the Kullback-Leibler distance and the Gini-Simpson index [20][21][22]. Ma studied how index TCDs are affected by a variable target centre determined by the desires or selection preferences of a decision maker (DM) with multiple-attribute decisionmaking (MADM) [19].…”