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 avail-able land resources for sustainavail-able 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 suit-ability 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 con-sidered 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
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1. Introduction
Land suitability evaluation for sustained crop production involves the interpreta-tion of data relating to soils, vegetainterpreta-tion, 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 pro-ductivity 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 lim-itations 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. LetUbe 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. x2A) and members {x} do not belong to crisp setAif 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 mem-bership) 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,
membership ofx in Awith each point in x (Pal and Majumdar, 1986). This char-acteristic 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 eventA
becomes higher. For example, A xi 1; indicates that it is strictly a member of that class andA 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 suit-ability evaluation oers a promising basis for rational selection of the crops. Theo-charopoulos et al. (1995) highlighted the merit of GIS in soil survey and land evaluation in Greece. They also listed the limitations of Boolean approach com-pared 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 fea-ture 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®edn number of land parameters,x x1;x2;. . .;xn, into mnumber
of suitability classes,i 1; 2;. . .; mfor 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 ofmclasses and nine parameters. To classify each pixel into one of themsuitability classes, following the land char-acteristics 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,xand class representative vector,c, as:
dE x; c
The smaller the distance, the more similarxis tocin 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:
wherefc xis the membership grade of pixel (x) in suitability class (c) andmis the number of suitability classes. From the above, it may be noted that for a given crop
c,mnumber of membership functions exist formsuitability classes, i.e. each pixel hasmmembership grades indicating the extent to which the pixel belongs to each of themclasses.
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 devia-tion 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:
Xn
i1
Wi1 3
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 ofnparameters constructed based on the Saaty's scaling ratios (Rao et al., 1991), which could be of the order (nxn) as:
A aij;i;j1;2;3;. . .;n; 4
where
aijWi=Wjfor alliandj: 5
aij1=aij; 6
andaijaik=ajkfor anyi; jandk: 7
Thus, multiplying Eq.(4) with the weighting factorwof (nx1) size yields:
AÿnIW0 8
whereIis 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 matrixAis, 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:
AWlmaxW; 9
whereA* is the estimate ofA, andW* is the corresponding priority vector andlmax is the largest eigen value for the matrixA. Eq.(9) yields the weightagesWwhich 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
Table 1
Saaty's importance scale
Intensity of importance
De®nition Explanation
1 Parameters are of equal importance Two parameters contribute equally to the objective
3 ParameterIis of more importance compared to parameterJ
Experience and judgement strongly favour IoverJ
5 Essential or strong importance ofI compared toJ
Experience and judgement strongly favour IoverJ
7 Very strong or demonstrated
importance
CriteriaIis very strongly favoured over Jand its dominance is demonstrated in practice
9 Absolute importance The evidence favouringIoverJto the
highest possible order of armation 2,4,6,8 Intermediate values between two
adjacent judgement
approach for crop-land suitability in assigning appropriate weightages for the var-ious 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 13804000 N to 1301104000 N, and longitude 77701200 E to 771103400 E, as shown in Fig. 1. The drainage of Kalyanakere sub-watershed is of sub-dendritic type. The physiography of the area is mostly undulat-ing with gently slopundulat-ing pediments and valleys occurrundulat-ing at an altitude rangundulat-ing from 820 to 1000 m above msl. There are hillocks and rock outcrops towards the north-east 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 (Anon-ymous, 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.
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 culti-vable 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.
Fig. 2. Contour map (5 m interval).
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 Win-dows 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 themclasses 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 accor-dance 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 param-eters 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 factorWj (see Section 4.1) to take into account the degree of dependence of crop-land suitability with reference to the particular crop-land characteristic parameter,j, as:
dEx; c
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).
dE x;c 0andfc x 1; 11
i.e. the membership grade of the pixel in classcis unity and grades in other classes are zero, which means that the pixel is exactly categorised into classc. 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
Table 2
Land suitability for (a) ®nger millet, (b) paddy and (c) ground nut Ð criteria and ratings
Site characteristics Suitable rating
Gravel Ð Surface (%) <5 5±15 15±35 35±80 >80
Gravel Ð Sub-surface (%) <15 15±35 35±75 >75 ±
pH 5.5±7.0 5.0±5.5 <5.0 ± ±
7.0±8.0 >8.0
CEC (meq/100 g) >24 24±16 16±10 10±5 <5
Base saturation (%) >80 80±50 50±35 <35 ±
(b) Paddy
Gravel Ð Surface (%) <5 5±15 15±35 35±50 >50
Gravel Ð Sub-surface (%) <10 10±35 35±40 50±75 >75
±
pH 5.5±6.5 5.5±5.0 5.0±4.0 4.0±3.4 ±
6.5±7.2 7.2±0.0 >8.0
CEC (meq/100 g) >24 24±16 16±10 10±5 >5
Base saturation (%) >80 80±50 50±35 >35 ±
(c) Ground nut
Texture Ð Sub-surface Gc, gcl, sc, sic c, sl heavy clay, ±
gsc, scl, ls, s
cl, sicl
Gravel Ð Surface (%) 0±15 15±35 35±50 50±75 >75
Gravel Ð Sub-surface (%) 15±35 35±50 50±75 >75 ±
0±15
pH 5.3±6.6 5.3±5.0 5.0±4.5 <4.5 ±
6.6±7.0 7.0±8.0 >8.0
CEC (meq/100 g) >24 24±16 16±10 <10 ±
an area (pixel) for dierent crops so that the crop of highest suitability can be found. The suitability of an area (pixel),x, for a crop,c, can be de®ned as:
S x;c 1=p xjÿcjt xjÿcj; 12
and the relative suitability of the area (pixel) for crop,i, as:
Ri x Si x=
Xc
j1
S x;j; 13
where,Ri(x) is the relative suitability membership function, which ranges from 0.0 to 1.0.
For obtaining the highest suitability for a given crop, the membership function map of highest suitability (S1) is obtained for each of the three crops. Thus, each pixel in these maps is associated with three membership grades, which indicate the highest suitability of the pixel for the three crops, respectively. To produce the map of highest suitability among the three crops, the maximum membership value among the three crops is assigned to each pixel.
5. Results and discussion
In the present study the fuzzy membership approach to crop-land suitability analysis is applied to assess: (1) the suitability class ratings (from highest 1 to lowest 5) for three crops, ®nger millet, ground nut and paddy; and (2) the highest suitable crop for a given area from amongst the three crops. The area outside the watershed being zero and water bodies assigned a value of 1, the ®ve suitability classes are assigned values from 2 to 6, and the rock outcrops as 7. As such, for normalisation, the minimum and maximum (range) membership values of pixels within the water-shed, but not falling under categories 1 and 7, are found and normalisation is done using this range to scale the values from 0.0 to 1.0.
5.1. Suitability class ratings for the three crops
5.2. Highest suitable crop
For determining the highest suitable crop for each pixel, the highest suitability rating maps (S1) are generated for the three crops, viz. ®nger millet (S1±C1), paddy (S1±C2) and ground nut (S1±C3) (see Section 4.3). Amongst the three crop suit-ability maps, the highest suitable crop is determined on the basis of largest mem-bership value and a map is generated showing the highest suitable crop for each pixel (Fig. 9a). The per cent areal coverages of the maximum suitability crops are given in the legend of the map.
Table 3
Important matrix for suitability of (a) ®nger millet, (b) paddy and (c) ground nut
Parametera 1(S1) 2(Drg) 3(TxtS) 4(TxtSS) 5(GrS) 6(GrSS) 7(PH) 8(CEC) 9(BS) Weights
(a) Finger millet
a Sl, slope; Drg, drainage; TxtS, surface texture; TxtSS, subsurface texture; GrS, surface gravel; GrSS,
5.3. Crop suitability assessment with weightage factors
As discussed earlier, Wang's approach for the computation of Euclidean distance implicitly assigns equal weightages to the deviation of each of the pixel parameter values from the speci®ed land suitability class values. In other words, two pixels having the same membership function values may belong to two dierent combi-nations as follows: one pixel may have a larger deviation for a crop important parameter and smaller deviation for a not so important parameter; the other pixel may have a smaller deviation for the crop important parameter and larger deviation for the not so important parameter. However, the two pixels may have the same Euclidean distance resulting in the same membership value for each pixel. But in reality, the second pixel must have a higher membership value in relation to the ®rst pixel judging from the suitability point of view of the crop and may sometimes have a higher or lower class rating. These likely variations are analysed with and without weightage factors in Wang's approach for the Kalyanakere sub-watershed.
Dierent parameters have dierent relative importances and, therefore, it is necessary to assign appropriate weightages to the parameters. To take care of these relative importances Saaty's method (see Section 1.3) is used to determine the weightage factors (Table 3). These weights are used in computing the Euclidean
Table 4
Representative matrix of suitability class and parameter values for (a) ®nger millet, (b) paddy and (c) ground nut
a P1, base saturation; P2, cation exchange capacity; P3, drainage; P4, pH; P5, stope; P6, surface gravel;
distances while determining the membership functions. Figs. 6b, 7b and 8b are the highest class suitability maps for the three crops, respectively, using weightages. The areal coverages of the suitability classes are given in the legend of these. The bar graphs (Figs. 6d, 7d and 8d) alongside these maps illustrate the changes in per cent areas between the two approaches, viz. with and without weights.
Figs. 6c, 7c and 8c are the maps derived by overlaying and cross-classifying the maps without weights (Figs. 6a, 7a and 8a ) and with weights (Figs. 6b, 7b and 8b). The legend gives the changes in per cent areal coverages of each of the suitability classes for the three crops. The bar graphs (Figs. 6e, 7e and 8e) adjacent to the cross-classi®cation maps (Figs. 6c, 7c and 8c) illustrate these changes.
The highest suitability crop assessment is also carried out without weights (Fig. 9a) and with weights (Fig. 9b). The per cent areal coverages of the dierent crops are given in the legends of these maps. The bar graph (Fig. 9d) adjacent to these two maps illustrates these coverages. Fig. 9c is the overlay and cross-classi®ed map of Fig. 9a and b, and shows the changes in per cent areal coverages of the crops. The bar graph (Fig. 9e) adjacent to this map illustrates these changes.
5.4. The eect of weightage factors on fuzzy classi®cation
As mentioned earlier, the three main crops considered in the present studies for fuzzy member classi®cation include ®nger millet, paddy and ground nut.
It can be seen from the highest suitability membership classi®cation (single crop) maps, viz. C1S1, C2S1 and C3S1 (see Section 5.2), that without considering weightages the per cent areas of ®nger millet, paddy and ground nut are 31.2, 37.12 and 60.12, respectively (Figs. 6a, 7a and 8a) and there are only two suitability classes, S1 and S2. However, with weightages, the per cent areas of these crops are 46.49, 12.67 and 73.8, respectively (Figs. 6b, 7b and 8b) and there are two or more classes in each category, i.e. two classes (S1 and S2) for ®nger millet, ®ve classes (S1, S2, S3, NI, N2) for paddy and four classes (S1, S2, S3, NI) for ground nut. The bar graphs (Figs. 6d, 7d and 8d) illustrate the per cent areas of these classes without (left) and with (right) weightage factors considered, and the middle bar showing the per cent areas remaining unchanged (common). Figs. 6c, 7c and 8c are cross-classi®cation maps showing the losses from and gains to the individual classes. There are losses to S1 and S2, i.e. pixels from these classes are classi®ed into other classes, for example, from S1 to S2, and S2 to S1 for ®nger millet, from S1 to S2, S3, NI, N2, and from S2 to S1, S3, NI, N2 for paddy and from S2 to S1, S3, NI for ground nut, as illustrated by the bar graphs (Figs. 6a, 7e and 8e). The losses from and gains to the classes indicate that there are substantial changes in the locations of areas of these classes, even though the net changes appear smaller. In addition, new classes have emerged in the maps with weightage factors (S3, NI, N2).
The results of the two approaches, viz. the highest suitable membership class approach, and highest suitable crop approach, have shown that there are marked changes in the areas of suitability with and without considering the weightage fac-tors. It is found from the ground truth information that the per cent areas of highest suitability match better with those of maps with weightage factors considered, as per the land characteristics of these areas. The important observation that is arrived at from the results is that higher per cent areas are highly suitable for growing ground nut, though at present higher per cent area is cultivated with ®nger millet. Such information could be very bene®cial for the farmers and land managers for taking measures to grow appropriate crops in highest suitable areas or improve the areas to suit the desired crop, so as to derive optimum production.
6. Conclusions
1. The inclusion of the weightage factors derived from multi-criteria analysis in Wang's method of fuzzy membership assessment of crop-land suitability may be signi®cant and may result in the upgrading or degradation of the class values of the pixel as compared to the assessment without the weights.
2. Fuzzy membership approach allows consideration of partial memberships to obviate the limitations of classical classi®cation methods. GIS approach allows consideration of the spatial variability of relevant terrain and other param-eters. The merit of the combination of the two approaches is found to be advantageous for delineating areas of various suitability ratings to a given crop more accurately, so that measures could be taken to grow the crops best suited for a given area and also to improve the areas to suit a desired crop.
3. The approach is also found to be advantageous to determine the crops of highest suitability for a given area, so that decisions could be made to grow appropriate crops and derive optimum production.
4. As per the ®eld information, the crop grown in maximum area is ®nger millet. However, the results of the present study indicate that the maximum area is potentially suitable for growing ground nut. As such, optimum production may be derived by growing ground nut or the land characteristics may be modi®ed to grow any other crop in these areas.
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