Porwal, Alok 
  
The major part of the Aravalli province was covered by airborne magnetic surveys (1967-72) at flight intervals of 500 
m and 1 km and at an altitude varying from 60 m to 130 m. These data were processed and visually interpreted by the 
Airborne Mineral Surveys and Exploration (AMSE) wing of the Geological Survey of India, who divided the entire 
region into 37 magnetic zones on the basis of magnetic intensities, patterns and features in relation to the geology and 
structural features as displayed on the geological map (GSI, 1981). Each magnetic zone can therefore be interpreted as a 
lithologic-tectonic-metallogenic association with a characteristic magnetic response. The spatial association of magnetic 
zones and base metal deposits was studied both empirically and genetically, and it was found that mineralisation tends 
to associate with particular magnetic zones. The magnetic zones map was, therefore, selected as one of the evidential 
maps. 
The evidence theme maps, which were originally digitised and reclassified as polygon shapes, were converted into grid 
themes with a grid size of 100 metres. The grid size was decided on the basis of resolutions (or scales) of input maps. 
The input evidence grid maps and the mineral distribution in the area are shown in Figs. 2 (A to F) 
3 FUZZY MODEL 
If X is a multi-class evidential data set whose classes are denoted generically by x, then a fuzzy set A in X, consisting 
of favourable indicators of mineralisation, can be defined such that 
À- ous QI xe X] 
Hz (x) is called the membership function or grade of membership (also degree of compatibility or degree of truth) of x 
in A which maps X to the membership space M (Zimmermann, 1985). When M contains only two points O and 1, A 
is non-fuzzy and U i (x) is identical to the characteristic function of a non-fuzzy set. 
Given two or more multi-class maps with fuzzy membership values for each class, these can be combined using a 
variety of fuzzy set operators. Zimmermann (1985) gives a variety of combination rules based on fuzzy mathematics. 
An et al. (1991) discuss five operators that were found useful for combining exploration datasets, viz., fuzzy AND, 
fuzzy OR, fuzzy algebraic product, fuzzy algebraic sum and fuzzy gamma (y) operator. Bonham-Carter (1994) gives a 
review of these operators. 
We used fuzzy the 'y operator function (Zimmermann and Zysno, 1980) for combining the maps. This operator is 
defined as follows: 
y 
m (1-7) n 
Ma en [Élu] (I) ; (1) 
where xeX, 0€ yx 1 
The y operator is a combination of the fuzzy algebraic product and fuzzy algebraic sum operators. At y= 0, the operator 
is equivalent to the fuzzy algebraic product, while at Y= 1, it is equivalent to fuzzy algebraic sum. This operator tends to 
compensate the "decreasive" tendency of fuzzy algebraic product with the “increasive” effect of fuzzy algebraic 
product. 
We used the following function to calculate fuzzy membership values: 
0 for Si = S rin 
5 San 
H a (x ÿ ) = S S for Sax? S S uin (2) 
1 — 
for Sij = Sax 
The Score (S;;) measures the effective weight of the i” class of the evidential map J, and was calculated using following 
relation: 
W, xW, 
EM. 
j^ 
Here W; is the weight of the i” class and W; is the weight of j^ map. These weights were assigned subjectively, based on 
past exploration experience and opinion of the experts. The scores and fuzzy membership values for each of the input 
maps are given in Table 1. 
$, 
y 
(3) 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 1181