International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
4. Calculate the dependent index of every attribute. The 
dependent index of every sub attribute can be obtained from 
the determined conditions. Certainly, the importance of 
attribute @ can be expressed by analyzing the quotient of 
posg. 4. (C) and posg CJ; 
5. When removing the attribute whose dependent index is 0, 
the positive domain of C/C is not affected. Therefore, 
according to the order of the priori weight, remove the 
attribute whose dependent index is 0 and whose priori weight 
is minimum. 
6. Calculate the core of every decision rule and its possible 
reduction forms. 
7. Select the attribute reduction table of effective decision rule 
according to certain principles and obtain the minimum rule. 
In practice, there may exist a very big rule set in step 7. Except 
for the specific cases of decision-making,such a big set is 
troublesome in practice. So, the most effective subset of 
attribute should be considered to correctly reduce or 
approximatly express the domain set. Generally, we judging a 
target, people would first take the atrribute with largest weight 
according to their priori knowledge into consideration. 
Thereby, we should select the reduction rules of the attributes 
with lager weights to represent the decision rule of the domain 
set. The following is a practical and effective method. 
Assuming that the reduced decision attribute set is |laj,a5,... 
Am their priori weight are p(ai),p(a»),...p(as), respectively,and 
rule i probably has k reduction form, then the definition of the 
weight of each form is: 
P = J (00a ) x"pta.» 
Here,if a is an appointed value, then Of(aj-1; if not an 
appointed value, then Ofa)=0. Last, combing the reduction 
forms with lagest weight to obtain a practical and effective 
decision rule set. 
5. CASE STUDY 
Taking the land use decision support system as an example, we 
discuss the problem on the proper types of crops in a certain 
type of soil. 
In Table !, cz. c» c; c, are the condition attributes; d is the 
decision-making attribute.c, indicates the elevation,c; soil type, 
€; crop type; c, annual average temperature and d output. 
  
  
  
nie he dd Te À cw 
] 50 Red Rice 25 Few 
2 10 Brown Wheat 12 Few 
3 240 Red Wheat 15 Few 
4 320 Brown Wheat 13 Lot 
5 400 Black ~~ Sorghum 5 Few 
6 900 Brown Rice 26 Few 
7 600 Brown Wheat 18 Lot 
8 1250 Brown Rice 22 Lot 
9 1300 Black Wheat 11 Few 
10 1400 Red Rice 2] Few 
  
  
Table 1. Spatial Object Information Tables 
Standardize the above table according to the classification 
standard: 
Elevation: 0: [0, 100] , 1: [ 100, 500], 2: [ 500, 1200 |, 
3:4 1200, »]; 
soil type: 0 : Red, 1: Brown, 2 : Black: 
256 
Crop type: 0: Rice, 1: Wheat, 2: Sorghum: 
Annual average temperature: 0: [-10, 10], 1 : [10, 20], 
2: [20, 1]: 
Output: 0: Few, 1: Lot 
Then we have Table 2. 
  
  
  
U | €) | Ca | €; Cy | d 
1 0 0 0 D 0 
2 0 ] ] 1 0 
3 1 () | ] 0 
4 I | l 1 1 
5 1 2 2 0 0 
6 2 1 0 2 0 
7 2 1 ] 1 1 
8 3 1 0 2 1 
9 3 2 1 1 0 
10 3 0 0 2 0 
  
  
Table 2. Spatial information table after standardization 
The weights of the attributes arc listed as 
c1=0.35, c,=0.3, c3=0.2, c4=0.15i 
Analyzing the attribute one by one,we obtain the dependent 
index. 
Let C ={cy.c2,03,04},D ={d}, then the dependent index of D on 
C CF=card(CND)/card(C)=1. We can see that the data views 
are inclusive.To cl,the dependent index of D on cl is 
CF. =card(C.; N 
D)/card(C,)=S/8.Similarly,CF.,= 1/2 CF.4=0,CF,4=0. 
According to the weights of the attributes,we can conclude that 
weight of attribute c; is larger than that of c4. Therefore, c; is 
remained while c, is removed. In the data view without ca, we 
can find that the dependent index of each attribute is greater 
than 0. So, each item can not be omitted. However, to obtain the 
reduced decision rule,we need to remove the unnecessary 
conditions in every decision rule, namely calculating the core of 
cach rule. 
To decision rule 1, 
F={{1],[1]en[1)e3}=141,2},{1.3,10}.{1,6,8,10} }, 
Le. [1]. 2:511). [1]511,2,3,5,6,9,101. 
To find the unnecessary attributes of dicision rule 1,we should 
check whether the intersection of other attributes’ subset is 
within the decision attributc’s sub-set [1], . 
[Ha Eom 3. Da EE (03, Ho01)37 (1107, 
Then we can find the core of decision rule 1 is empty,which 
can be expressed in three forms: ¢;(1)=0 and ¢5(1)=0,c5(1) = 0 
and ¢;(1)=0, c,(1)=0 and c-(1)=0. 
Similarly, we can obtain the core of each rule and its reduced 
form, listed in Table 3 and Table 4. 
  
  
  
UT WI | Cy | d 
] X X X 0 
2 0 X X 0 
3 X 0 X 0 
4 l J X 1 
5 x X X 0 
6 X X X 0 
7 2 X X l 
8 X l X l 
9 X X X 0 
10 X X X 0 
  
  
Table 3. Reduced spatial information table 
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