Construction of CCTWF Evaluation of the Modernization of Hydraulic Projects Management Compact-Center-Point Triangular Whitenization Weight Function

 ISSN: 1693-6930 TELKOMNIKA Vol. 13, No. 4, December 2015 : 1478 – 1485 1479

2. Construction of CCTWF

S. F. Liu et al. have constructed the grey clustering evaluation method based on ETWF and that based on CTWF [3,4]. In practical use, the division of grey clustering intervals in these existing triangular whitenization weight functions is short of scientificity. In response to this shortage, on the basis of analyzing the overlapping properties, the clustering coefficients, the division of grey clustering intervals and the selection of endpoints in these functions, this paper improves the existing functions and constructs CCTWF. The calculation procedure of the grey clustering evaluation model based on CCTWF is as follows: Assuming there is an object set O = {Oi| i = 1, 2, …, n }, which is clustered into different grey clusters of s, and s ∈ {1,2,3,4}. Then g = {gj| j =1, 2, …, m } is the evaluation index set of an object Oi. ij x , i = 1,2, …, n; j =1,2, …, mi are the observation values of an object Oi for clustering index gj. The corresponding object Oi can be evaluated according to the observation value ij x . In order to describe it correctly, any object Oi ∈ O is taken as an example. The following is the procedure: Step 1: Determine the 1 2 , , , s ij ij ij     be the grey center points of the clustering index gj of the object Oi , and the value range allowed for ij x is 1 1 [ , ] s ij ij a a  , thus we can get the center points 1 , s ij ij    by extending grey clusters toward different directions. Step 2: Let 1 , 1, 2, , 2 k k ij ij k ij b k s        , then we get the interval 1 , k k ij ij b b      . Assuming   1 max , k k k k k ij ij ij ij b b        ,   1 min , k k k k ij ij        , then we identify the grey interval of the cluster k is     1 , , k k k k k k k k ij ij ij ij c c                 . Special note: if 1 2 k k ij ij k ij b b     , then   k k k ij ij c b  , and   1 1 k k k ij ij c b    . Let the grey interval of the cluster k be     1 , k k k k ij ij c c      , connect the points     , 0 k k ij c ,   ,1 k ij  , and     1 , 0 k k ij c  , then we can get the triangular whitenization weight function of the index j on the grey cluster k is   , 1, 2, , , 1, 2, , , 1, 2, , k ij f i n j m k s        . For an observation value ij x of the index j, we can prove that its degree of membership to the grey cluster   =1 2 k k s ，，…， is   k ij ij f x by the following formulas:                    1 1 1 1 0, , , , , , k k ij k k ij ij k ij k k ij k k ij ij ij k ij k ij k ij k ij k k ij k ij k ij ij k k ij k k ij ij x c c x c f x x c c c x x c c                                          1 TELKOMNIKA ISSN: 1693-6930  Evaluation of the Modernization of Hydraulic Projects Management Compact-… Li Lijie 1480 Step 3: The integrated clustering coefficients of the object   =1 2 i i n ，，…， belonging to the grey cluster k can be calculated by :   1 m k k i ij ij ij j f x      2 Where   k ij ij f x is the triangular whitenization weight function of the index j belonging to the grey cluster k, and ij  is the weight of the object i belonging to the index j in comprehensive clustering. Step 4: Because of   1 max k k i i k s      , we can say that the object i belongs to the grey cluster k  . It means that when more than one objects belong to the grey cluster k  , we can sort these objects according to the size of the integrated clustering coefficients, and then determine the precedence or quality of each object which belongs to the grey cluster k  . 3. Division of Grey Clustering Intervals There is no pragmatic way of selecting ETWF’s end points 1 2 1 2 , , , , , , s s s a a a a a a    , and the division of grey clusters is lack of scientific evidence. Also, CTWF lets k  , which is most likely to belong to the grey cluster k , be the end point of that grey cluster, so it’s more apt to get each grey cluster’s triangular whitenization weight functions based on 1 2 1 , , , , , s s        . [5, 6] In fact, in accordance with their thinking habits, people have more accurate understanding and judgment of grey clustering end points than those of grey clustering intervals, and CTWF is superior to ETWF on endpoints selection. But the division of grey cluster CTWF lacks scientificity. Let 1 2 , , , s ij ij ij     be the grey center points of the clustering index gj of the object Oi, and the range of value allowed for ij x is 1 1 [ , ] s ij ij a a  . According to the construction methods of CTWF and CCTWF, the grey intervals of the grey cluster k are  1 1 , k k ij ij      and      1 , k k k k ij ij c c    , respectively, and it is clear that       1 1 1 , , k k k k k k ij ij ij ij c c           . Thus for the same grey interval, the grey interval length divided by CCTWF is smaller, the crossing area of grey haze set is diminished, the calculation efficiency is increased, meanwhile it further differentiates index observation value’s membership grade for each grey cluster, and thus ensures the conclusion’s reliability.

4. Case Study