18 Table 1 Entities with 3 indicators
Entity
Ranking
Indicator1 Indicator2 Indicator3 A
1.5 2
3 B
3 5
4 C
1.5 3
2 D
8 6
7 E
7 8
6
Figure 6 X-shaped Hasse diagram of five entities labeled as A, B, C, D and E
2.2.2 Subordination Schematic and ORDIT
Subordination can be symbolized diagrammatically Wayne and Patil 2010
in a triangle depicted in Figure 7, where the point with coordinates SS, AA
representing a sub district makes a triangle divided into two parts, ‘trapezoidal
triplet’ of AA, SS, and II and a topping triangle of CCC and II. The
combination of th
ese two parts forms a right triangle with the ‘tip’ at AA = 100 in the upper-left and the toe at SS = 100 in the lower-right. The hypotenuse is a
right-
hand ‘limiting line’ of plotting positions because AA+SS+II=100. Topping
triangle provides the basis for an ‘ORDIT ordering’ of the districts or instances.
According to the Figure 7, an idealized district has AA = 100 of the deleted domain DD of other districts, that is the frequency of ascribed advantage being
equal to the number of competing districts, so if the ideal actually occurs, then the trapezoidal triplet becomes a triangle.
19
Figure 7 Subordination schematic with plotted instance dividing a right triangle
into two parts, a ‘trapezoidal triplet’ of AA, SS and II below, and a ‘topping triangle’ of CCC, SS and II above.
The numbers for ORDIT can be coupled as a decimal value ccc.bbb. The ccc component is obtained by rounding CCC to two decimal places and then
multiplying by 100. The bbb component is obtained by dividing SS by CCC, and imposing 0.999 as an upper limit. And then add these two values as ccc.bbb. This
ordering is assigned the acronym ORDIT and preserves all aspects of AA, SS and II
except for the actual number of districts. Simple rank ordering of ORDIT values becomes salient scaling of the district Myers and Patil 2010.
2.2.3 Product-order Rating Regime
A general relational rule for ascribing advantage is product-order whereby advantage is gained by having all criteria at least as good and at least one better.
Conversely, subordinate status lies with having all criteria at least as poor and at least one poorer. This relational rule is applicable to all kinds of criteria as long as
they have the same polarity sense of better and worse. Scheme 2 Myers and
Patil 2010 in Function Facilities gives an R function called ProdOrdr that
determines ORDITs and salient scaling according to product-order. This function takes as its inputs a vector of IDs for instances, a data frame of same-sense criteria.
All indicators are either positive sense or negative sense. Indicators in this research are negative indicators which means that the larger the value of the indicators, the
20 more severe the district. The output is a data frame of ORDITs and salient scaling
values According to Figure 7 and its computation, ORDIT ordering is the ranking of
the instances based on their indicators. ORDITs and salient scaling according to product-order are determined by Scheme 2 Myers and Patil 2010 in Function
Facilities of R function. ORDIT is topping triangle in Figure 7 and Salient is the
ranking of ORDIT.
Precedence Plots
Based on computation of AA and SS for a particular district, the structure in
the lower part of the subordination schematic can be used to prepare a ‘precedence plot’ for visualization. The precedence plot is a plot for AA ascribed advantage
as Y-axis and SS subordinate status as the X-axis. Prominent position declines from top upper-left to toe lower-right. Primary prominence varies vertically
showing that there is a larger percentage of ascribed advantage greater severity with increasing height. Horizontal variation on a given level shows clarity of
comparison. Farther to the right is greater clarity as more definite advantage less severe with a larger percentage of subordinate status versus indefinite instances
among the couplets where ascribed advantage is lacking. In other words, more indefinite instances constitute increased lack of clarity incomparability in the
usual parlance of partial ordering. Scheme 3 Myers and Patil 2010 in Function Facilities gives an R function named PrecPlot which accepts the output of the
ProdOrdr function and produces a precedence plot.
Representative Ranks Representative ranks show descriptive statistics of indicator rankings of each
district. In other words, representative ranks show descriptive statistics for each district according to ranking of indicators. The function of representative ranks is
to see how crucial a district is. The rank numbers received by a given district across all criteria can be placed in a single array and sorted in ascending order.
With place-based ranks, the maximum of these will reflect an important
21 component for the case. This computation is effective for several indicators.
Because the only two indicators, this study did not raise this calculation
2.2.4 The concepts of Askeskin or HIP and Surkin or PL
