Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol63.Issue2.Feb2000:
Agricultural Systems 63 (2000) 75±95
www.elsevier.com/locate/agsy
GIS-based fuzzy membership model for
crop-land suitability analysis
T.R. Nisar Ahamed, K. Gopal Rao, J.S.R. Murthy *
Department of Civil Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India
Received 4 December 1998; received in revised form 16 May 1999; accepted 17 June 1999
Abstract
Crop-land suitability analysis is a prerequisite to achieve optimum utilisation of the available land resources for sustainable agricultural production. The Food and Agricultural
Organisation [FAO, 1976. A framework for land evaluation (Soils Bulletin No. 32). FAO,
Rome.] recommended an approach for land suitability evaluation for crops in terms of suitability ratings from highly suitable to not suitable based on climatic and terrain data and soil
properties crop-wise. The assignment of a given area element (pixel) to any one suitability
class is encountered with problems due to the variation of soil properties within the area as
well as matching of the soil properties with more than one suitability class to dierent extents.
The Boolean methods are designed to assign a pixel to a single class and no provision exists
for assigning partial suitability to each of the appropriate suitability classes. In the present
study the use of fuzzy (partial) membership classi®cation is used to accommodate the above
uncertainty in assigning the suitability classes to the pixel. The evaluation of the spatial
variability of relevant terrain parameters is carried out in a geographic information system
environment while assigning the land suitability for crops in the study area of Kalyanakere
sub-watershed in Karnataka. Nine parameters (eight of soil and one of topography) are considered and suitability analysis is carried out by fuzzy membership classi®cation with due
weightage factors included to accommodate the relative importance of the soil parameters
governing the crop productivity. According to the ®eld information, the crop being grown in
maximum area is ®nger millet. However, the crop-land evaluation results of the present study
reveal that maximum area is potentially suitable for growing ground nut. # 2000 Elsevier
Science Ltd. All rights reserved.
Keywords: Land evaluation; Suitability criteria; Classi®cation; Fuzzy membership; GIS
* Corresponding author. Tel.: +91-22-578-2545; fax: +91-22-578-3480.
E-mail address: [email protected] (J.S.R. Murthy).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00036-0
76
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
1. Introduction
Land suitability evaluation for sustained crop production involves the interpretation of data relating to soils, vegetation, topography, climate, etc., during an eort
to match the land characteristics with crop requirements (Wang et al., 1990). Based
on the suitability of land characteristics to dierent crops, the Food and Agricultural
Organisation (FAO, 1976) proposed land evaluation in terms of two broad classes,
`suitable' (S) and `not suitable' (N). These two are further sub-classi®ed as follows:
Class S1 Ð Highly suitable: land having no signi®cant limitations for sustained
applications to a given use, or only minor limitations that will not signi®cantly
reduce the productivity.
Class S2 Ð Moderately suitable: land having limitations that in the aggregate are
moderately severe for sustained application to a given use and may reduce the productivity marginally. These lands have slight limitations and/or no more than three
moderate limitations.
Class S3 Ð Marginally suitable: land with limitations that in the aggregate are severe
for sustained application to a given use and as such reduce productivity signi®cantly
but is still marginally economical. These lands have more than three moderate limitations and/or more than one severe limitation that, however, does not preclude their
use for the speci®ed purposes.
Class NI Ð Currently not suitable: land that has qualities that appear to preclude
sustained use of the kind under consideration.
Class N2 Ð Permanently not suitable.
The attributes of the above land suitability criteria are to be derived from both
spatial and non-spatial information under diverse and multiple criteria. Geographic
information systems (GIS) are best suited for handling both spatial and non-spatial
data, with due consideration for the spatial variability of the terrain and other
attributes for an ecient time and cost-eective evaluation.
1.1. Fuzzy sets and fuzzy membership
Fuzzy set theory was introduced by Zadeh (1965) and the de®nitions of fuzzy set
and fuzzy membership (Kauman and Gupta, 1985; Zimmermann, 1985) are as
follows. Let U be a universe of a collection of distinct objects. In the present context,
the universe is a map, the sets are landuse classes and elements are the pixels. A crisp
set A consists of members {x} if the characteristic function A x 1 (i.e. x 2 A)
and members {x} do not belong to crisp set A if A x 0. Thus the boundary of
set A is rigid and sharp. Fuzzy set eliminates the sharp boundary that divides
members from non-members in the group by providing a transition (partial membership) between the full membership and non-membership (Wang, 1990).
A fuzzy set (A) in a space of points, x fxg; is a class of events with a continuum
of grades of membership. The fuzzy set is characterised by a membership function,
A x, which associates a real number in the interval (0,1) representing the grade of
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
77
membership of x in A with each point in x (Pal and Majumdar, 1986). This characteristic function, in fact, can be viewed as a weighting coecient which re¯ects the
ambiguity in a set and as it approaches unity; the grade of membership of an event A
becomes higher. For example, A xi 1; indicates that it is strictly a member of
that class and A xi 0 indicates that it is not a member of that class.
1.2. Land suitability and fuzzy membership approach
Chang and Burrough (1987), Burrough (1989), Burrough et al. (1992), Tang et al.
(1991) and Tang and Van Ranst (1992) suggest that the fuzzy method of land suitability evaluation oers a promising basis for rational selection of the crops. Theocharopoulos et al. (1995) highlighted the merit of GIS in soil survey and land
evaluation in Greece. They also listed the limitations of Boolean approach compared to fuzzy set in land evaluation. Wang et al. (1990) described a method of fuzzy
information representation and processing in a GIS context, which lead to the
development of a fuzzy suitability rating method. In view of the characteristic feature of transitional or continuous variation in the geographical phenomena such as
rock types, soil or vegetation classes, Burrough and McDonnell (1998) expressed
that fuzzy membership approach, which retains the complete information of partial
memberships giving due consideration to the uncertainty involved, is appropriate in
de®ning the boundaries between dierent classes.
Following the arable land±crop suitability consideration of FAO, Wang et al.
(1990) classi®ed n number of land parameters, x x1 ; x2 ; . . . ; xn , into m number
of suitability classes, i 1 ; 2 ; . . . ; m for the chosen crop. Thus, the suitability
of the land (in terms of magnitude of the parameters) to suit the crop (prototype
vector) is represented as a two dimensional matrix of m classes and nine parameters.
To classify each pixel into one of the m suitability classes, following the land characteristics and criteria, a measure of similarity is calculated between the pixel vector
and the class vector as its suitability rating. The similarity measure between the pixel
vector and the representative class vector is determined (Wang et al., 1990) by the
Euclidean distance between the pixel vector, x and class representative vector, c , as:
v"
#
u n
u X
p
xj ÿ cj 2 or xj ÿ cj t xj ÿ cj :
1
dE x; c t
j1
The smaller the distance, the more similar x is to c in terms of land characteristics.
Once the Euclidean distance is de®ned, the fuzzy membership grade of the pixel (x)
for a suitability class is given by:
1
d x c
;
fc x m E
P
1
i1 dE x i
2
78
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
where fc x is the membership grade of pixel (x) in suitability class (c) and m is the
number of suitability classes. From the above, it may be noted that for a given crop
c, m number of membership functions exist for m suitability classes, i.e. each pixel
has m membership grades indicating the extent to which the pixel belongs to each of
the m classes.
Suitability in the above context is to be understood as the potential suitability of
an area for given uses through the modi®cation of one or more land attributes, such
as reduction of water saturation of soil by drainage or reducing excessive slope by
terracing (Wang et al., 1990).
While calculating the membership value of the pixel by Eq. (2), the computation
of the Euclidean distance by Eq. (1) implicitly assigns equal weightage to the deviation of each of the pixel parameter class values from the speci®ed land suitability
class values. Thus, the same value of the Euclidean distance may result from several
equally likely combinations of the deviations of the pixel parameter class values
from the speci®ed land suitability class values and hence, is not a unique value to
describe the degree of crop-land suitability in the computation of the membership
value by Eq. (2).
1.3. Multi-criteria suitability analysis for crops and land
One of the classical problems in decision theory or multi-parameter analysis is the
determination of the relative importance of each parameter. The relative importance
of parameters vis-aÁ-vis the objective is usually represented by a set of weights, and
are normalised to a constant or unity, as:
n
X
Wi 1
3
i1
Saaty's (1980) analytical hierarchy process is a method to determine the weights,
as follows.
An importance scale is proposed for the pair-wise comparison of parameters,
based on a large number of experiments (Table 1). In the eigen vector method for
the determination of the largest eigen value to estimate the weights, the basic input
is the pair-wise comparison matrix of n parameters constructed based on the Saaty's
scaling ratios (Rao et al., 1991), which could be of the order (nxn) as:
A aij ; i; j 1; 2; 3; . . . ; n;
4
where
aij Wi =Wj for all i and j:
5
The matrix A generally has the property of reciprocality and also consistency, i.e.
mathematically:
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
79
Table 1
Saaty's importance scale
Intensity
of importance
De®nition
Explanation
1
Parameters are of equal importance
3
Parameter I is of more importance
compared to parameter J
Essential or strong importance of I
compared to J
Very strong or demonstrated
importance
Two parameters contribute equally to the
objective
Experience and judgement strongly favour
I over J
Experience and judgement strongly favour
I over J
Criteria I is very strongly favoured over
J and its dominance is demonstrated in
practice
The evidence favouring I over J to the
highest possible order of armation
Judgement is not precise enough to assign
values of 1,3,5,7 and 9 (compromise is needed)
5
7
9
Absolute importance
2,4,6,8
Intermediate values between two
adjacent judgement
aij 1=aij ;
6
and aij aik =ajk for any i; j and k:
7
Thus, multiplying Eq.(4) with the weighting factor w of (nx1) size yields:
A ÿ nIW 0
8
where I is an identity matrix of (nxn). According to matrix theory, if the comparison
matrix A has the property of consistency, the system of equations has a trivial
solution. The matrix A is, however, a judgement matrix and it may not be possible
to determine the elements of A accurately to satisfy the property of consistency.
Therefore, it is estimated by a set of linear homogeneous equations:
A W lmax W ;
9
where A* is the estimate of A, and W* is the corresponding priority vector and lmax
is the largest eigen value for the matrix A. Eq.(9) yields the weightages W which are
normalised to unity.
2. Objectives
The objective of the present study is to evaluate the arable land suitability for the
given crops, viz. ®nger millet, paddy and ground nut, using fuzzy membership and
GIS approach. Due consideration is given for the relative importance of the soil
parameters while deciding the partial membership values. Thus, an attempt is made
in the study to draw on the multi-criteria suitability approach and fuzzy membership
80
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
approach for crop-land suitability in assigning appropriate weightages for the various soil parameters while computing the partial membership values for each of the
arable crop-land classes.
3. The study area
The study area is the Kalyanakere sub-watershed No. 1, which is spread over 2200
ha, covered under Survey of India (SOI) topographic map No. 57 G/4 in Karnataka
State, India. It is bounded by latitude 13 80 4000 N to 130 110 4000 N, and longitude
77 70 1200 E to 77 110 3400 E, as shown in Fig. 1. The drainage of Kalyanakere subwatershed is of sub-dendritic type. The physiography of the area is mostly undulating with gently sloping pediments and valleys occurring at an altitude ranging from
820 to 1000 m above msl. There are hillocks and rock outcrops towards the northeast parts of the watershed. Generally the relief of the area is normal in pediments
and valleys and excessive in hilly terrain. From the available 5-m interval contour
map (Fig. 2) of the study area, a contour Digital Elevation Model (DEM) (Fig. 3)
was generated from which a grid DEM was derived and the slope data was obtained.
The various soil series and landuse information is available at 1:8000 scale (Anonymous, 1992). The study area falls in the eastern partially dry agricultural zone in
Karnataka, India, and it is predominately a Kharif (cropped during monsoon) zone.
Fig. 1. Location map of study area.
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
81
Fig. 2. Contour map (5 m interval).
Fig. 3. Digital Elevation Model of study area.
The landuse map was compiled for the year 1993. Over the entire watershed (2250
ha), the two major landuse categories are cultivable dry land (72.42%) and cultivable wet land (11.94%). The major crops grown under dry land agriculture in the
area are ®nger millet and ground nut while paddy is grown in the wet lands under
assured irrigation.
82
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
4. Methodology
In the present study, nine soil parameters, such as texture, soil drainage, Cation
Exchange Capacity (CEC), base saturation, slope, gravelliness and pH values, are
chosen for crop-land suitability analysis and thematic maps are developed for each of
the parameters. All the maps are rasterised and co-registered using IDRISI for Windows GIS software (Eastman, 1997) with the same spatial resolution of 14.514.5 m
on the ground that resulted in 390 rows (lines) and 548 columns (pixels). These maps
are reclassed again based on the suitability criteria (Table 2a±c) for the chosen crops.
Thus, a total of 27 reclassed parameter maps are developed. The prototype vectors
representing the m classes and nine parameters are presented in Table 4a±c for the
three crops.
The various steps involved in the land suitability analysis are shown in the ¯ow
chart (Fig. 4). The computations are made in two stages: (1) suitability ratings for a
given crop; and (2) highest suitability for the given number of crops.
4.1. Weightage factors for the land parameters
To evaluate the weightage factors to be assigned to the soil parameters in accordance with the importance of each parameter governing the crop, the multi-criteria
suitability analysis (see Section 1.3) is adopted. Pair-wise comparison matrix (Table
3) is prepared using Saaty's analytical hierarchical process (Table 1). Eigen value
method is used to determine the weightage factors for each of the nine soil parameters considered (Table 3).
4.2. Suitability ratings/partial membership values for a given crop
The fuzzy membership approach for crop-land suitability is based on Eqs. (1)
and (2). As a modi®cation to the method proposed by Wang (1990), the Euclidean
distance in the present study is proposed to be computed by including a weightage
factor Wj (see Section 4.1) to take into account the degree of dependence of cropland suitability with reference to the particular land characteristic parameter, j, as:
v"
#
u n
u X
Wj2 xj ÿ cj 2 :
dE x; c t
10
n1
Once the Euclidean distance is related to the importance of the parameter, the
fuzzy membership grade of the pixel (x) for suitability class is given by Eq.(2).
From the above, it can be seen that for a given crop c, m number of membership
functions exist corresponding to the m number of suitability classes, i.e. each pixel
has m membership grades indicating the extent to which the pixel belongs to each of
the classes. Further, if the pixel vector is equal to the representative vector of the
suitability class, c, then:
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
83
Fig. 4. Fuzzy membership and GIS approach for land suitability analysis. DEM, Digital Elevation
Model; CEC, cation exchange capacity; GIS, geographical information system.
dE x; c 0 and fc x 1;
11
i.e. the membership grade of the pixel in class c is unity and grades in other classes are
zero, which means that the pixel is exactly categorised into class c. The steps involved
in suitability class membership approach are given in the ¯ow chart (Fig. 5).
4.3. Relative suitability and crop of highest suitability
Relative suitability assessment helps in production of a potential landuse map
based on land suitability for dierent crops, viz. ®nger millet, paddy and ground
nut. In this case, instead of suitability classes, dierent crops are de®ned as fuzzy
sets. The fuzzy partition method, as above, is used to assess the relative suitability of
84
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
Table 2
Land suitability for (a) ®nger millet, (b) paddy and (c) ground nut Ð criteria and ratings
Site characteristics
Suitable rating
Suitable
Not suitable
S1
S2
S3
N1
N2
(a) Finger millet
Land
Slope (%)
Drainage class
1±3
5
3±5
4
5±10
3, 6
10±15
2, 7
>15
0, 1
Soil
Texture Ð Surface
Texture Ð Sub-surface
Gravel Ð Surface (%)
Gravel Ð Sub-surface (%)
pH
sil, l, sl
c, sic, sc
24
>80
ls, sic, c
ls, sl
15±35
35±75
8.0
16±10
50±35
s, heavy clay
S
35±80
>75
±
CEC (meq/100 g)
Base saturation (%)
cl, scl, sicl
cl, scl, sicl
5±15
15±35
5.0±5.5
7.0±8.0
24±16
80±50
10±5
24
>80
5.5±5.0
6.5±7.2
24±16
80±50
5.0±4.0
7.2±0.0
16±10
50±35
sl, ls
s
35±50
50±75
±
4.0±3.4
>8.0
10±5
>35
(c) Ground nut
Land
Slope (%)
Drainage class
1±3
5
3±5
4, 6
5±10
3, 7
10±15
1, 2
>15
±
scl, cicl
sc, sic
sl, sc, s
c, sl
sic, c
heavy clay,
ls, s
s
±
Gravel Ð Surface (%)
Gravel Ð Sub-surface (%)
sl, l, sil
Gc, gcl,
gsc, scl,
cl, sicl
0±15
15±35
15±35
35±50
50±75
>75
>75
±
pH
5.3±6.6
>24
>80
8.0
www.elsevier.com/locate/agsy
GIS-based fuzzy membership model for
crop-land suitability analysis
T.R. Nisar Ahamed, K. Gopal Rao, J.S.R. Murthy *
Department of Civil Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India
Received 4 December 1998; received in revised form 16 May 1999; accepted 17 June 1999
Abstract
Crop-land suitability analysis is a prerequisite to achieve optimum utilisation of the available land resources for sustainable agricultural production. The Food and Agricultural
Organisation [FAO, 1976. A framework for land evaluation (Soils Bulletin No. 32). FAO,
Rome.] recommended an approach for land suitability evaluation for crops in terms of suitability ratings from highly suitable to not suitable based on climatic and terrain data and soil
properties crop-wise. The assignment of a given area element (pixel) to any one suitability
class is encountered with problems due to the variation of soil properties within the area as
well as matching of the soil properties with more than one suitability class to dierent extents.
The Boolean methods are designed to assign a pixel to a single class and no provision exists
for assigning partial suitability to each of the appropriate suitability classes. In the present
study the use of fuzzy (partial) membership classi®cation is used to accommodate the above
uncertainty in assigning the suitability classes to the pixel. The evaluation of the spatial
variability of relevant terrain parameters is carried out in a geographic information system
environment while assigning the land suitability for crops in the study area of Kalyanakere
sub-watershed in Karnataka. Nine parameters (eight of soil and one of topography) are considered and suitability analysis is carried out by fuzzy membership classi®cation with due
weightage factors included to accommodate the relative importance of the soil parameters
governing the crop productivity. According to the ®eld information, the crop being grown in
maximum area is ®nger millet. However, the crop-land evaluation results of the present study
reveal that maximum area is potentially suitable for growing ground nut. # 2000 Elsevier
Science Ltd. All rights reserved.
Keywords: Land evaluation; Suitability criteria; Classi®cation; Fuzzy membership; GIS
* Corresponding author. Tel.: +91-22-578-2545; fax: +91-22-578-3480.
E-mail address: [email protected] (J.S.R. Murthy).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00036-0
76
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
1. Introduction
Land suitability evaluation for sustained crop production involves the interpretation of data relating to soils, vegetation, topography, climate, etc., during an eort
to match the land characteristics with crop requirements (Wang et al., 1990). Based
on the suitability of land characteristics to dierent crops, the Food and Agricultural
Organisation (FAO, 1976) proposed land evaluation in terms of two broad classes,
`suitable' (S) and `not suitable' (N). These two are further sub-classi®ed as follows:
Class S1 Ð Highly suitable: land having no signi®cant limitations for sustained
applications to a given use, or only minor limitations that will not signi®cantly
reduce the productivity.
Class S2 Ð Moderately suitable: land having limitations that in the aggregate are
moderately severe for sustained application to a given use and may reduce the productivity marginally. These lands have slight limitations and/or no more than three
moderate limitations.
Class S3 Ð Marginally suitable: land with limitations that in the aggregate are severe
for sustained application to a given use and as such reduce productivity signi®cantly
but is still marginally economical. These lands have more than three moderate limitations and/or more than one severe limitation that, however, does not preclude their
use for the speci®ed purposes.
Class NI Ð Currently not suitable: land that has qualities that appear to preclude
sustained use of the kind under consideration.
Class N2 Ð Permanently not suitable.
The attributes of the above land suitability criteria are to be derived from both
spatial and non-spatial information under diverse and multiple criteria. Geographic
information systems (GIS) are best suited for handling both spatial and non-spatial
data, with due consideration for the spatial variability of the terrain and other
attributes for an ecient time and cost-eective evaluation.
1.1. Fuzzy sets and fuzzy membership
Fuzzy set theory was introduced by Zadeh (1965) and the de®nitions of fuzzy set
and fuzzy membership (Kauman and Gupta, 1985; Zimmermann, 1985) are as
follows. Let U be a universe of a collection of distinct objects. In the present context,
the universe is a map, the sets are landuse classes and elements are the pixels. A crisp
set A consists of members {x} if the characteristic function A x 1 (i.e. x 2 A)
and members {x} do not belong to crisp set A if A x 0. Thus the boundary of
set A is rigid and sharp. Fuzzy set eliminates the sharp boundary that divides
members from non-members in the group by providing a transition (partial membership) between the full membership and non-membership (Wang, 1990).
A fuzzy set (A) in a space of points, x fxg; is a class of events with a continuum
of grades of membership. The fuzzy set is characterised by a membership function,
A x, which associates a real number in the interval (0,1) representing the grade of
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
77
membership of x in A with each point in x (Pal and Majumdar, 1986). This characteristic function, in fact, can be viewed as a weighting coecient which re¯ects the
ambiguity in a set and as it approaches unity; the grade of membership of an event A
becomes higher. For example, A xi 1; indicates that it is strictly a member of
that class and A xi 0 indicates that it is not a member of that class.
1.2. Land suitability and fuzzy membership approach
Chang and Burrough (1987), Burrough (1989), Burrough et al. (1992), Tang et al.
(1991) and Tang and Van Ranst (1992) suggest that the fuzzy method of land suitability evaluation oers a promising basis for rational selection of the crops. Theocharopoulos et al. (1995) highlighted the merit of GIS in soil survey and land
evaluation in Greece. They also listed the limitations of Boolean approach compared to fuzzy set in land evaluation. Wang et al. (1990) described a method of fuzzy
information representation and processing in a GIS context, which lead to the
development of a fuzzy suitability rating method. In view of the characteristic feature of transitional or continuous variation in the geographical phenomena such as
rock types, soil or vegetation classes, Burrough and McDonnell (1998) expressed
that fuzzy membership approach, which retains the complete information of partial
memberships giving due consideration to the uncertainty involved, is appropriate in
de®ning the boundaries between dierent classes.
Following the arable land±crop suitability consideration of FAO, Wang et al.
(1990) classi®ed n number of land parameters, x x1 ; x2 ; . . . ; xn , into m number
of suitability classes, i 1 ; 2 ; . . . ; m for the chosen crop. Thus, the suitability
of the land (in terms of magnitude of the parameters) to suit the crop (prototype
vector) is represented as a two dimensional matrix of m classes and nine parameters.
To classify each pixel into one of the m suitability classes, following the land characteristics and criteria, a measure of similarity is calculated between the pixel vector
and the class vector as its suitability rating. The similarity measure between the pixel
vector and the representative class vector is determined (Wang et al., 1990) by the
Euclidean distance between the pixel vector, x and class representative vector, c , as:
v"
#
u n
u X
p
xj ÿ cj 2 or xj ÿ cj t xj ÿ cj :
1
dE x; c t
j1
The smaller the distance, the more similar x is to c in terms of land characteristics.
Once the Euclidean distance is de®ned, the fuzzy membership grade of the pixel (x)
for a suitability class is given by:
1
d x c
;
fc x m E
P
1
i1 dE x i
2
78
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
where fc x is the membership grade of pixel (x) in suitability class (c) and m is the
number of suitability classes. From the above, it may be noted that for a given crop
c, m number of membership functions exist for m suitability classes, i.e. each pixel
has m membership grades indicating the extent to which the pixel belongs to each of
the m classes.
Suitability in the above context is to be understood as the potential suitability of
an area for given uses through the modi®cation of one or more land attributes, such
as reduction of water saturation of soil by drainage or reducing excessive slope by
terracing (Wang et al., 1990).
While calculating the membership value of the pixel by Eq. (2), the computation
of the Euclidean distance by Eq. (1) implicitly assigns equal weightage to the deviation of each of the pixel parameter class values from the speci®ed land suitability
class values. Thus, the same value of the Euclidean distance may result from several
equally likely combinations of the deviations of the pixel parameter class values
from the speci®ed land suitability class values and hence, is not a unique value to
describe the degree of crop-land suitability in the computation of the membership
value by Eq. (2).
1.3. Multi-criteria suitability analysis for crops and land
One of the classical problems in decision theory or multi-parameter analysis is the
determination of the relative importance of each parameter. The relative importance
of parameters vis-aÁ-vis the objective is usually represented by a set of weights, and
are normalised to a constant or unity, as:
n
X
Wi 1
3
i1
Saaty's (1980) analytical hierarchy process is a method to determine the weights,
as follows.
An importance scale is proposed for the pair-wise comparison of parameters,
based on a large number of experiments (Table 1). In the eigen vector method for
the determination of the largest eigen value to estimate the weights, the basic input
is the pair-wise comparison matrix of n parameters constructed based on the Saaty's
scaling ratios (Rao et al., 1991), which could be of the order (nxn) as:
A aij ; i; j 1; 2; 3; . . . ; n;
4
where
aij Wi =Wj for all i and j:
5
The matrix A generally has the property of reciprocality and also consistency, i.e.
mathematically:
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
79
Table 1
Saaty's importance scale
Intensity
of importance
De®nition
Explanation
1
Parameters are of equal importance
3
Parameter I is of more importance
compared to parameter J
Essential or strong importance of I
compared to J
Very strong or demonstrated
importance
Two parameters contribute equally to the
objective
Experience and judgement strongly favour
I over J
Experience and judgement strongly favour
I over J
Criteria I is very strongly favoured over
J and its dominance is demonstrated in
practice
The evidence favouring I over J to the
highest possible order of armation
Judgement is not precise enough to assign
values of 1,3,5,7 and 9 (compromise is needed)
5
7
9
Absolute importance
2,4,6,8
Intermediate values between two
adjacent judgement
aij 1=aij ;
6
and aij aik =ajk for any i; j and k:
7
Thus, multiplying Eq.(4) with the weighting factor w of (nx1) size yields:
A ÿ nIW 0
8
where I is an identity matrix of (nxn). According to matrix theory, if the comparison
matrix A has the property of consistency, the system of equations has a trivial
solution. The matrix A is, however, a judgement matrix and it may not be possible
to determine the elements of A accurately to satisfy the property of consistency.
Therefore, it is estimated by a set of linear homogeneous equations:
A W lmax W ;
9
where A* is the estimate of A, and W* is the corresponding priority vector and lmax
is the largest eigen value for the matrix A. Eq.(9) yields the weightages W which are
normalised to unity.
2. Objectives
The objective of the present study is to evaluate the arable land suitability for the
given crops, viz. ®nger millet, paddy and ground nut, using fuzzy membership and
GIS approach. Due consideration is given for the relative importance of the soil
parameters while deciding the partial membership values. Thus, an attempt is made
in the study to draw on the multi-criteria suitability approach and fuzzy membership
80
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
approach for crop-land suitability in assigning appropriate weightages for the various soil parameters while computing the partial membership values for each of the
arable crop-land classes.
3. The study area
The study area is the Kalyanakere sub-watershed No. 1, which is spread over 2200
ha, covered under Survey of India (SOI) topographic map No. 57 G/4 in Karnataka
State, India. It is bounded by latitude 13 80 4000 N to 130 110 4000 N, and longitude
77 70 1200 E to 77 110 3400 E, as shown in Fig. 1. The drainage of Kalyanakere subwatershed is of sub-dendritic type. The physiography of the area is mostly undulating with gently sloping pediments and valleys occurring at an altitude ranging from
820 to 1000 m above msl. There are hillocks and rock outcrops towards the northeast parts of the watershed. Generally the relief of the area is normal in pediments
and valleys and excessive in hilly terrain. From the available 5-m interval contour
map (Fig. 2) of the study area, a contour Digital Elevation Model (DEM) (Fig. 3)
was generated from which a grid DEM was derived and the slope data was obtained.
The various soil series and landuse information is available at 1:8000 scale (Anonymous, 1992). The study area falls in the eastern partially dry agricultural zone in
Karnataka, India, and it is predominately a Kharif (cropped during monsoon) zone.
Fig. 1. Location map of study area.
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
81
Fig. 2. Contour map (5 m interval).
Fig. 3. Digital Elevation Model of study area.
The landuse map was compiled for the year 1993. Over the entire watershed (2250
ha), the two major landuse categories are cultivable dry land (72.42%) and cultivable wet land (11.94%). The major crops grown under dry land agriculture in the
area are ®nger millet and ground nut while paddy is grown in the wet lands under
assured irrigation.
82
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
4. Methodology
In the present study, nine soil parameters, such as texture, soil drainage, Cation
Exchange Capacity (CEC), base saturation, slope, gravelliness and pH values, are
chosen for crop-land suitability analysis and thematic maps are developed for each of
the parameters. All the maps are rasterised and co-registered using IDRISI for Windows GIS software (Eastman, 1997) with the same spatial resolution of 14.514.5 m
on the ground that resulted in 390 rows (lines) and 548 columns (pixels). These maps
are reclassed again based on the suitability criteria (Table 2a±c) for the chosen crops.
Thus, a total of 27 reclassed parameter maps are developed. The prototype vectors
representing the m classes and nine parameters are presented in Table 4a±c for the
three crops.
The various steps involved in the land suitability analysis are shown in the ¯ow
chart (Fig. 4). The computations are made in two stages: (1) suitability ratings for a
given crop; and (2) highest suitability for the given number of crops.
4.1. Weightage factors for the land parameters
To evaluate the weightage factors to be assigned to the soil parameters in accordance with the importance of each parameter governing the crop, the multi-criteria
suitability analysis (see Section 1.3) is adopted. Pair-wise comparison matrix (Table
3) is prepared using Saaty's analytical hierarchical process (Table 1). Eigen value
method is used to determine the weightage factors for each of the nine soil parameters considered (Table 3).
4.2. Suitability ratings/partial membership values for a given crop
The fuzzy membership approach for crop-land suitability is based on Eqs. (1)
and (2). As a modi®cation to the method proposed by Wang (1990), the Euclidean
distance in the present study is proposed to be computed by including a weightage
factor Wj (see Section 4.1) to take into account the degree of dependence of cropland suitability with reference to the particular land characteristic parameter, j, as:
v"
#
u n
u X
Wj2 xj ÿ cj 2 :
dE x; c t
10
n1
Once the Euclidean distance is related to the importance of the parameter, the
fuzzy membership grade of the pixel (x) for suitability class is given by Eq.(2).
From the above, it can be seen that for a given crop c, m number of membership
functions exist corresponding to the m number of suitability classes, i.e. each pixel
has m membership grades indicating the extent to which the pixel belongs to each of
the classes. Further, if the pixel vector is equal to the representative vector of the
suitability class, c, then:
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
83
Fig. 4. Fuzzy membership and GIS approach for land suitability analysis. DEM, Digital Elevation
Model; CEC, cation exchange capacity; GIS, geographical information system.
dE x; c 0 and fc x 1;
11
i.e. the membership grade of the pixel in class c is unity and grades in other classes are
zero, which means that the pixel is exactly categorised into class c. The steps involved
in suitability class membership approach are given in the ¯ow chart (Fig. 5).
4.3. Relative suitability and crop of highest suitability
Relative suitability assessment helps in production of a potential landuse map
based on land suitability for dierent crops, viz. ®nger millet, paddy and ground
nut. In this case, instead of suitability classes, dierent crops are de®ned as fuzzy
sets. The fuzzy partition method, as above, is used to assess the relative suitability of
84
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 75±95
Table 2
Land suitability for (a) ®nger millet, (b) paddy and (c) ground nut Ð criteria and ratings
Site characteristics
Suitable rating
Suitable
Not suitable
S1
S2
S3
N1
N2
(a) Finger millet
Land
Slope (%)
Drainage class
1±3
5
3±5
4
5±10
3, 6
10±15
2, 7
>15
0, 1
Soil
Texture Ð Surface
Texture Ð Sub-surface
Gravel Ð Surface (%)
Gravel Ð Sub-surface (%)
pH
sil, l, sl
c, sic, sc
24
>80
ls, sic, c
ls, sl
15±35
35±75
8.0
16±10
50±35
s, heavy clay
S
35±80
>75
±
CEC (meq/100 g)
Base saturation (%)
cl, scl, sicl
cl, scl, sicl
5±15
15±35
5.0±5.5
7.0±8.0
24±16
80±50
10±5
24
>80
5.5±5.0
6.5±7.2
24±16
80±50
5.0±4.0
7.2±0.0
16±10
50±35
sl, ls
s
35±50
50±75
±
4.0±3.4
>8.0
10±5
>35
(c) Ground nut
Land
Slope (%)
Drainage class
1±3
5
3±5
4, 6
5±10
3, 7
10±15
1, 2
>15
±
scl, cicl
sc, sic
sl, sc, s
c, sl
sic, c
heavy clay,
ls, s
s
±
Gravel Ð Surface (%)
Gravel Ð Sub-surface (%)
sl, l, sil
Gc, gcl,
gsc, scl,
cl, sicl
0±15
15±35
15±35
35±50
50±75
>75
>75
±
pH
5.3±6.6
>24
>80
8.0