Comparison of Boolean and fuzzy classification methods in land suitability analysis by using geographical information systems

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1 Environment and Planning A, 1992, volume 24, pages Comparison of Boolean and fuzzy classification methods in land suitability analysis by using geographical information systems G B Hall Faculty of Environmental Studies, University of Waterloo, Waterloo, Ontario N2L3G1, Canada F Wang School of Engineering, University of Guelph, Guelph, Ontario N1G 2W1, Canada Subaryono Department of Geography, University of Waterloo, Waterloo, Ontario N2L3G1, Canada Received 14 September 1990; in revised form 5 July 1991 Abstract. In this paper the information content of Boolean and fuzzy-set-based approaches to the problem of analyzing land suitability for agriculture within a geographical information system (GIS) is assessed. First, the two approaches to this problem are stated and formalized in the context of land-suitability evaluation. A database comprising 642 unique areas, 7 land qualities, 13 land characteristics, and 2 crop types is defined and described. Land-use suitability ratings for two crops, wetland rice and soybean, are generated by using Boolean and fuzzy methods. Results produced by the two methods are compared in terms of their usefulness for agricultural land-use plannning. The ARC/INFO vector-based GIS software package is utilized. The study area is the Cimanuk watershed in northwest Java, Indonesia. 1 Introduction In an earlier paper (Wang et al, 1990) we defined and tested a fuzzy relational data model in the context of assessing land suitability for agriculture in the Cimanuk watershed, northwest Java, Indonesia. In that paper we argued that the use of fuzzy information and processing offers more realistic information for land-use decisionmaking than Boolean processing methods, which are available in all conventional geographic information systems (GISs). Fuzzy techniques were shown to provide realistic results by obtaining membership grades for 642 unique areas in 4 mutually exclusive land-suitability classes (, highly suitable;, moderately suitable; S3, marginally suitable; N, unsuitable). Such processing als determination of the extent to which a particular area belongs to a suitability class for a given crop, rather than simply whether or not the area belongs to the suitability class for that crop. Compared with the conventional agricultural suitability classification method, which rates an area according to its most limiting quality (FAO, 1982), the fuzzy pattern recognition method we used takes into consideration all physiographic characteristics for which data are available and als decisionmakers the added ability to describe areas by using fuzzy concepts such as 'somewhat' highly suitable or 'very' 'highly suitable in assessing land characteristics according to crop growth requirements. The model and analysis in our earlier paper works equally well for individual crops in absolute terms or for the relative suitability of several crops together. Such information als land-use decisionmakers to make optimal multiple-purpose use of valuable land resources. It is therefore implied, although not explicitly demonstrated, in our earlier paper that fuzzy representation and processing have considerable advantages over the more commonly used Boolean processing procedures.

2 498 G B Hall, F Wang, Subaryono In this paper, we extend our earlier discussion and analysis by contrasting Boolean and fuzzy processing and assessing their relative usefulness for decisionmakers. In particular, we focus on two crops, wetland rice and soybean, of central importance in the Cimanuk watershed area. The database comprises the same 642 areas, 7 land qualities, and 13 land characteristics described in our earlier paper. In this case, we assess the current land suitability for each crop and the effect of improvements on modifiable limiting factors to produce results for potential land-use suitability for each crop. By examining both the Boolean and the fuzzy cases the advantages of the latter are shown explicitly and convincingly. In the foling section we review methods of land evaluation for agriculture. The Boolean case is presented in the context of the UN Food and Agriculture Organization (FAO) framework for land evaluation (FAO, 1976). This is foled by a review and statement of the fuzzy suitability method for analyzing current and potential land-use suitability. The study area and database common to each method are briefly described in section 5. In sections 6 and 7 we present and discuss the results of Boolean and fuzzy analyses. The paper is summarized and concluded in section 8. 2 Methods of land evaluation A basic feature of land evaluation is the comparison of the requirements of a particular land use with the resources offered by an area of land (Davidson, 1986). Fundamental to the evaluation process is the fact that different kinds of land uses have different requirements (Dent and Young, 1981). The objective of land evaluation, therefore, is to match, as accurately and efficiently as possible, land-use requirements and land characteristics in order to provide planners and decisionmakers with the ability to make comparisons and to identify promising alternative courses of action (Beek, 1978; McRae and Burnham, 1981). Recognizing this objective, FAO introduced in 1976 its now widely used framework for land evaluation. Several principles, fundamental to the process of land evaluation, are identified in this framework. Specifically, land suitability must be assessed and classified with respect to specified kinds of use; evaluation must be undertaken in terms relevant to the physical, economic, and social context of the area concerned; suitability must take into account use on a sustained basis; and evaluation must involve comparison of more than a single kind of use. The structure introduced by FAO identifies four hierarchical categories of land suitability into which individual areas of land are placed based upon their characteristics relative to the requirements of a given land use. At the top of the hierarchy, land-suitability orders indicate whether land is assessed as suitable or not for a given use. There are two orders recognized within the FAO framework, namely order S (suitable) and order N (not suitable). The former is land on which the kind of use under consideration will yield benefits without unacceptable risk or damage to the land resource. The latter is land which has qualities that are inappropriate for the use under consideration on a sustained basis. At the next level, within land-suitability order S, there are three land-suitability classes, namely (highly suitable), (moderately suitable); and S3 (marginally suitable). Suitability order N has two classes, Nl (currently not suitable but the problem is potentially surmountable) and N2 (permanently unsuitable). For the purposes of this paper, suitability classes Nl and N2 are collapsed into one class N that includes permanently unsuitable and improvable land for each land use under examination. The FAO framework differentiates between land characteristics, defined as 'attributes of land that can be measured or estimated' and land qualities, defined as

3 Comparison of Boolean and fuzzy classification methods 499 'complex attributes of land which act in a distinct manner in their influence on the suitability of land for a specified kind of use* (Brinkman and Smyth, 1973; FAO, 1976; 1982). Examples of land characteristics include, among others, annual average rainfall and temperature, rooting depth of soil, and slope. When determining land suitability for any given purpose, a single land characteristic is unlikely to influence suitability independently, unless the characteristic is extreme, such as very high (or very ) temperature. Thus a single land characteristic should only rarely be used to define suitability classes. Rather, suitability should be determined by the interaction of land characteristics such as slope, soil permeability, soil structure, rainfall, and so on. The combination of such characteristics determines land qualities that may or may not be conducive to a given use. Land qualities are an intermediate step in determination of land suitability for agriculture and other uses. Unlike most land characteristics, qualities are not directly measured but are rated, by using the above scheme, as,, S3, or N. The process by which such rating occurs is by matching, in the case of agriculture, crop growth requirements with land characteristics, and rating suitability classes according to the match of land-use requirements with land qualities. The matching process has characteristically used the rules of Boolean algebra where class membership is mutually exclusive or 'crisp'. In the Boolean case an area of land can either be a member of a suitability class for a land quality or is excluded, depending on the match between land-characteristic requirements for the use in question and actual land conditions. No other cases are aled. Use of Boolean intersection, union and negation rules, membership or nonmembership of a class controls how data about land characteristics are combined to make statements about land qualities, and ultimately about land suitability (Chang and Burrough, 1987). The topological overlay capalilities of most conventional GIS packages make this computer-based technology an attractive means by which to undertake such analyses (for example, see Best and Westin, 1984; Burrough, 1987; demeijere et al, 1988). Boolean topological overlay is appealing in this case because of its apparent elegance and simplicity. The number of criteria that can be considered is, in principle, limitless as any level of detail can be attained. However, the simplicity of the approach, although being a major strength, is also a major weakness. In reality, land characteristics and qualities and crop growth requirements are not exactly definable entities. Moreover, the all-or-nothing mathematics of Boolean logic has been demonstrated to be inadequate for spatial analysis and planning in general (Leung, 1988) as well as spatial classification and boundary determination in particular (Leung, 1984; 1985; 1987). This is especially true in the case of land evaluation based on the process of polygon overlay, where it is not only assumed that all data required to characterize the problem at hand are available and are in digital form but also that the data are free from measurement errors. In reality neither assumption, and particularly the latter, is likely to be valid. In cases where appropriate data are available in either digital or analogue form there is often no means by which to judge their measurement and spatial registration accuracy. The Boolean method of land evaluation as conventionally applied within GIS, requires precise classification criteria and assumes accuracy in measurement and spatial registration. Methods based on fuzzy logic can al these needs and such limiting assumptions to be relaxed (Burrough, 1989; Chang and Burrough, 1987; Wang et al, 1990). In the next sections, we describe two methodologies for assessing agricultural land-use suitability. The Boolean procedure is described, foled by the definition of an equivalent but less restrictive and arguably more useful fuzzy set methodology.

4 500 G B Hall, F Wang, Subaryono 3 Boolean method of land-suitability evaluation for agriculture 3.1 Crop growth and suitability rating criteria Consistent with local crop requirements in Indonesia, the suitability rating framework used in this research is a derivative of the FAO model, developed jointly by the Indonesian Centre for Soil Research (CSR) and the Food and Agriculture Organization (CSR/FAO, 1983). The CSR/FAO model defines 15 land characteristics, grouped into 7 land qualities, which are matched against crop growth requirements for the crops of interest. The relevant land characteristics and qualities are defined in table 1. Suitability is classified at the FAO suitability class levels,, S3 and N, which reflect land suitability within each order S and N. In most but not all, cases, areas Table 1. Land characteristics and land qualities for determining crop suitability classes. Source: CSR/FAO, Land qualities Land characteristics t, Temperature regime w, Water availability r, Rooting conditions /, Nutrient retention n, Nutrient availability x, Toxicity s, Terrain Note: CEC, cation exchange capacity. Annual average temperature ( C) Dry months (<75 mm rainfall) Average annual rainfall (mm) Soil drainage class Soil texture (surface) Rooting depth (cm) CEC; me per 100 g soil (subsoil) ph (surface soil) Total nitrogen Available P Available K 2 0 Salinity mm hos cm" 1 (subsurface) Slope (%) Surface stoniness Rock outcrops Table 2. Growth requirements for wetland rice and soybeans. Source: CSR/FAO, Land characteristics grouped by land qualities Land-suitability ratings S3 N (a) Wetland rice Temperature regime, / Annual average temperature ( Water availability, w Dry months (<75 mm) Average annual rainfall (mm) Rooting conditions, r Soil drainage class Soil texture (surface) 3 C) >1500 somewhat poor, moderately well sandy clay loam, silt loam, silt, clay loam very poor, poor sandy loam, loam, silty clay loam, silty clay, structured clay well loamy sand, massive clay >35 <18 >9.5 <800 somewhat excessive, excessive gravels, sands

5 Comparison of Boolean and fuzzy classification methods 501 Table 2 (continued) Land characteristics grouped by land qualities Rooting depth (cm) Nutrient retention, / CEC me per loog soil (subsoil) ph (surface soil) Nutrient availability, n Total nitrogen (surface) Available P (surface) Available K 2 0 (surface) Toxicity, x Salinity mm hos cm" 1 (subsoil) Terrain, s Slope (%) Surface stoniness Rock outcrops (b) Soybean Temperature regime, / Annual average temperature ( C) Water availability, w Dry months (<75 mm) Average annual rainfall (mm) Rooting conditions, r Soil drainage class Soil texture (surface) Rooting depth (cm) Nutrient retention, / CEC me per 100 g soil (subsoil) ph (surface soil) Land-suitability ratings Nutrient availability, n Total nitrogen (surface) > medium Available P 2 O s (surface) >high Available K 2 0 (surface) >very Toxicity, x Salinity mm hos cm" * <2.5 (subsoil) Terrain, s Slope (%) 0-5 Surface stoniness 0 Rock outcrops 0 Note: CEC, cation exchange capacity. >50 > medium > medium very high > medium < moderately well, well loam, sandy clay loam, silt loam, silt, clay loam, silty clay loam >50 > medium *4-4.5 high somewhat excessive sandy loam, sandy clay medium S very very medium- very poor, somewhat poor loamy sand, silty clay, structured clay very very -very N <20 >8.5 <4.0 very >8 >8 >1 >2 >32 <18 >9.5 >3500 <500 very poor, excessive gravels, sands, massive clay <15 >8.5 <5.0 >8.0 >20 >2 >2

6 502 G B Hall, F Wang, Subaryono of land assessed as N for a given crop will have limitations so severe as to preclude any possibility of successful growth of that crop. Growth requirements for the two crops under consideration in this paper, wetland rice and soybean, are detailed in table 2. For each crop, column 1 identifies relevant land characteristics grouped by land qualities, and columns 2 through 5 list ratings for the 4 suitability classes. Inspection of table 2 indicates that even though each crop has its own critical values for determining the land-characteristic ratings, the pattern is similar. Land which has values either er or higher than the critical values determining rating will fall into a er suitability class. Also, some land characteristics such as number of dry months, toxicity level, and slope operate similarly in that higher land-characteristic values produce er suitability-class ratings. For rooting depth, cation exchange capacity (CEC), P 2 O s, and K 2 0, a er value will produce a er suitability rating. The land requirements for crop suitability stated in table 2 can be used to identify current land suitability and potential land suitability. The former refers to land in its present state without major improvements to limiting characteristics. The latter refers to the same land after implementing land-improvement schemes designed to overcome limiting factors. In each case, the est land-characteristic rating in a single land-quality class is taken as the rating for that quality. Logically, then, the est rating of all land qualities is the final suitability rating for a given land area. This procedure for current and potential suitability in the Boolean case is explained be. 3.2 Current land suitability To illustrate, consider the foling example for land-quality ratings for rooting condition. Rooting condition, r: Soil drainage class, ; Soil texture (surface), ; Rooting depth, S3. In this case, quality r will be rated S3 because of the rooting depth limitation. Similarly, if all qualities for the land area are rated as fols: t:, w:, r: S3, /:, n:, x:, s:, the area will be rated as marginally suitable, S3 r, with the subscript denoting the major limiting condition. Where more than one quality is rated as est, the relevant subscript is added to denote limitations. 3.3 Potential land suitability The limiting characteristics identified in current suitability analysis can vary in both their possibility of improvement and the level of inputs required to achieve improvement. For example, inadequate availability of nutrients can be improved by applying fertilizer, whereas annual average temperature cannot be artificially modified on a large scale. Improvements are also variable in terms of cost of materials and labor. Irrigation works, for example, designed to overcome annual average rainfall may be more expensive than application of fertilizer to overcome poor nutrient availability.

7 Comparison of Boolean and fuzzy classification methods 503 The possible improvements of land characteristics and the levels of improvement required to improve suitability levels for crops are shown in table 3. Combinations of improvements may be undertaken to enhance land suitability. Specifically, two or more input (LI) improvements constitute a moderate improvement (MI). Two or more moderate inputs constitute a high level of input (HI). A combination of and moderate inputs constitute a high input. If the limiting land quality or any combination of limiting qualities cannot be improved the symbol X is used to denote that no improvement is possible. Through application of improvements to limiting land qualities, the current suitability class for a crop can be increased by at least one class in potential suitability subject to the restrictions of nonmodifiable limitations. Thus, it is possible for an area of land currently rated as N (nonsuitable) for a crop to improve to (highly suitable) potential if there are no limitations to improvements in land qualities. Table 3. Possible land-characteristic improvements and the level of input required. Source: SCR/FAO, Land characteristics grouped by qualities Possible improvements Level of input Temperature regime, t Annual average temperature Water availability, w Dry months Average annual rainfall Rooting conditions, r Soil drainage class Soil texture Rooting depth Nutrient retention, f CEC ph Nutrient availability, n Total nitrogen Available P 2 O s Available K 2 0 Toxicity, x Salinity Terrain, s Slope Surface stoniness Rock outcrop Note: HI, high input; MI, No improvement possible Irrigation works Irrigation works Artificial drainage No improvement possible Generally no improvement possible if root-restricting layer is thick. If root-restricting layer is thin then mechanical breakup of the layer may be possible. Liming: source available locally Liming: no local source Liming: source available locally Liming: no local source Manure or fertilizer application Fertilizer application for rating Fertilizer application for rating Fertilizer application for S3 or N ratings Reclamation of saline: soil ratings or S3 soils rating N Sawah construction for wetland rice slopes <3% Sawah construction for wetland rice slopes 3-8% Contour grass strips slopes 0-8% Moderate standard bench terrace without designed water disposal, slopes >8% High standard bench terrace with fully designed water disposal, slopes > 8% Stone picking for ratings or S3 only No improvement possible medium input; LI, input. X HI HI HI X HI LI MI MI MI LI LI LI MI MI HI LI MI LI MI HI MI X

8 G B Hall, F Wang, Subaryono With 7 land qualities to consider in the overall suitability rating of an area of land for a crop there are many possible combinations of land qualities that have nonmodifiable limitations in classes, S3, and N. This number can be calculated by the combinatorial rule y, *! m NLR W.(N-R)\' where NC R is the number of combinations of IV possible limitations taking R limitations at a time. In classes, S3, and N, 127 different possible combinations of severe limitations can occur. This comprises the sum of all combinations of 1 through 7 land qualities for each class. 3.4 Boolean procedure The procedure foled to produce a Boolean analysis of land suitability involves topological overlay of 5 digital 'coverages' (temperature, rainfall, soil class, soil salinity, and slope class) in the GIS to produce a composite map. The composite coverage for the study area contains 642 combined polygons and an attribute table with information on all items present in the original coverages. It is assumed that the original data layers are accurate in terms of both measurement and spatial registration. However, because all data were obtained from secondary sources, there is no easy way to confirm this. The items, which are land characteristics, are then matched sequentially against the requirements for each crop to determine land-quality ratings. The matching process is performed by a database program and is precise. For example, in the case of wetland rice, if annual average temperature in an area is 29.9 C, suitability on this land quality is. If, however, temperature is higher on average by 0.01 C in another area the suitability class is for the crop on this land quality. No divergence from class membership is permitted. Such analyses, no matter how carefully conceived, impose unrealistic preciseness on crop growth conditions and hence on land-suitability analysis. An alternative to this procedure is to relax the strict Boolean rules to al for the more realistic case where partial classmembership functions can be defined. This is possible with fuzzy set theory (Zadeh, 1965). The fuzzy land-suitability evaluation method used in this paper is described be in section 4. 4 Fuzzy land-suitability evaluation for agriculture 4.1 Fuzzy geographical information representation Let Y be a universe of discourse, whose generic elements are denoted v. Thus, Y = {v}. Membership in a classical set A of Y is often viewed as a characteristic function % A from Y to {0, 1} such that % A {y) = 1 if and only if v e A. A fuzzy set (Zadeh, 1965) B in Y is characterized by a membership function f B which associates with each v a real number in [0, 1]. Function f B (y) represents the 'grade of membership' of y in B. The closer the value of f B {y) is to 1, the more y belongs to B. In contrast to a Boolean set, a fuzzy set does not have sharply defined boundaries and a set element may have partial membership. Geographical information that is portrayed spatially in cartographic form is conventionally represented by thematic maps. Currently, the linkages between the map spatial entities, namely, points, lines, and areas, and their nonspatial, discrete attributes are based on the membership concept of Boolean set theory. That is, an entity either has an attribute value entirely or does not have it at all. No third situation is aled. A major shortfall of such a representation method is that (1)

9 Comparison of Boolean and fuzzy classification methods 505 complex geographical phenomena, such as land-cover mixture and intermediate conditions, cannot be properly described. Fuzzy set theory can provide a better means of internal representation for geographical information. In a fuzzy representation, classes can be defined as fuzzy sets, and spatial entities as set elements. Each spatial entity is associated with a group of membership grades to indicate the extents to which the entity belongs to certain classes. Entities with class mixture or in intermediate conditions can be described by membership grades. For example, if a ground area contains a mixture of two land-cover classes, soil and grass, it may have two membership grades indicating the extents to which it is associated with the two classes. 4,2 Fuzzy suitability evaluation Fuzzy representation als us to develop a fuzzy method of land-suitability evaluation for agriculture that relaxes the strict membership conditions of Boolean algebra. The fuzzy method does not impose a sharp class boundary between 'suitable' and 'unsuitable' lands. The fact that an area is in an intermediate condition between 'suitable' and 'unsuitable' can be identified and described properly. After overlaying m coverages, an area in the composite map can be viewed as a vector in an ra-dimensional feature space: (a l9 a 2,..., a m ), where a t (1 < i < m) is value of the /th land characteristic of the area. In the rest of this paper, such a vector is referred to as an area vector. Representing areas as vectors enables a pattern recognition method to be used for land-suitability rating. The method developed in this research is characterized by a fuzzy partition of feature space. The task of land-suitability rating is to classify areas into classes,, S3, and N according to their land characteristics. In terms of the vectors, we can use a distance between an area vector and a class as a measure of their similarity. The similarity can then be used to indicate the extent to which the area belongs to the class. To measure the similarity, we define a representative vector (or prototype) for each class and use a distance between an area vector and the representative vector to measure the similarity between the vector and the class. The representative vector of class * (1 ^ / < 4), ju h is of the form {Pil,Mi2i»;Pim) T, (2) where m is the number of physiographic characteristics to be considered, and fiy is value of the yth characteristic of the requirements for suitability class / (1 < j < m). Let q be an area vector. The Euclidean distance between q and ju c may be expressed as d E (q,ju c ) = I ilj-vcj) (3) J - = [(g-mc) T (g-/ic)r, (4) and can be used to indicate the similarity between q and class c. The smaller the distance, the more similar q is to c in terms of the land qualities. The conventional classification rule based on this metric is: qe c iff d E (q, ju c ) <,d E (q, &), Vc # /. (5) This decision rule defines sharp decision surfaces between classes, such that a vector can be classified into a single class and the classification implies a full membership in that class. Such a method is referred to as a hard partition of feature space.

10 506 G B Hall, F Wang, Subaryono The pattern recognition method enables us to rate the suitability of an area by comprehensively taking into consideration all of its characteristics and all of the suitability classes. An area can be classified into the class to which it is most similar. However, a strict Boolean interpretation of class membership leads to serious loss of information. Let us take two areas as examples. In determining their suitability for a given crop, the distances from the vector of the first area to the 4 classes are 0.50, 0.40, 0.10, and 0.00, respectively. The distances from the vector of the second area to the classes are 0.90, 0.10, 0.00, and 0.00, respectively. According to the decision rule in equation (5), both areas are most similar to class. But, clearly, the first area is much less suitable for the crop than the second area. In the Boolean case, the information contained in the distances is discarded when the memberships of the areas are determined. To make fuller use of the information, a fuzzy partition of feature space is used as the preferred method of representation in this research. In a fuzzy partition, the classes are defined as fuzzy sets. An area can be associated with partial membership and belong to different classes to different extents. A fuzzy set is characterized by its membership function. We define the membership function f c for suitability class c as d E (q,ju c ) I, = 1 d E (q,pi) where p is the number of classes; the expression p i /=1 d E {q,jhi) serves as a normalizing factor; and f c {q) is the membership grade of area q in suitability class c. For a given crop, 4 membership functions are defined for the 4 suitability classes. By calculating the functions, we find each area has 4 membership grades indicating the extents to which this area belongs to each of the 4 classes. In the case that the physiographic characteristics of an area are precisely equal to those of the representative vector of suitability class c, that is, d E {q,mc) =0, the membership grade of the area in class c is defined as 1 and the grades in other classes as 0. This implies that this area can be exactly categorized into class c. This method is less sensitive to 'noises' in the data than the conventional method. For example, if the most restrictive characteristic value of an area is in but is recorded in N by mistake, the suitability class of the area is thus N according to the conventional Boolean method. In the pattern recognition method, each characteristic contributes 1/ra in calculating a distance. Hence, such a mistake will not dramatically change the suitability class of the area. 4.3 Current and potential land suitability Current land-suitability evaluation for an area is straightforward by using equation (6). The data describing the current situation of the area are used to calculate the distances and then the membership grades. Potential land-suitability evaluation for an area requires more calculation. First, limiting factors of the area are identified. If the limiting factors in an area are severe no improvement is possible when either crop is considered. If it is possible to improve the limiting factors for a crop, the most severe limitation is identified.

11 Comparison of Boolean and fuzzy classification methods 507 The most limiting factor is a) if a i -ju u > aj-pu,' for j = 1,2,..., m, where ju u is the ith characteristic of the representative vector of, namely, the highly suitable class. Then a t is assigned with a new value which is usually one class better than the current one. The potential land suitability is evaluated on the 'improved' value of a t with the rest of the values unchanged. The membership grades calculated by use of equation (6) describe the potential suitability of the area. 5 Study area and data The Cimanuk watershed is located in northwest Java, Indonesia. The area is characterized by recent land-use change resulting from increased population density, river sedimentation, and soil salinization along the northern (coastal) boundary. A total of 4 major land uses are found in the watershed sawah (rice fields), settlements with homestead gardens, homestead gardens, and mixtures of swamp, grass, and fish ponds. The pressure on land through increased settlement has resulted in conversion of rice fields to settlements and depletion of mangrove forests for rice fields and fish ponds. In particular, during the past 45 years the areas of forest and sawah'have decreased by 95% and 11%, respectively (Sigalingging, 1985). Currently, sawah represents 76.5% of the area, settlements with homestead gardens 6.4%, and homestead gardens 8.2%. The remaining area is used variously as forest, shrubs, grass, swamp, and fish ponds. In physiographic terms, the watershed is mainly a flat coastal plain with elevations generally less than 25 meters. There is little annual variation in the mean monthly temperature of 27 C, with an equally small diurnal temperature range. Precipitation occurs in 3 to 4 consecutive months foled by at least 6 months of dry weather (Oldeman, 1975). September has the est monthly rainfall, and December and January are the wettest months. Dent et al (1977) describe the physiography of the area in terms of 4 'land systems' that comprise natural landscape units identified by their genesis and geomorphological distinctiveness. The land systems are the delta area of the Cimanuk river; the central alluvial part of the coastal plain; the upper eastern part of the coastal plain; and the upper western complement of the coastal plain. The most immature soils are found, as to be expected, in the delta area and the most mature are on the upper western part of the coastal plain. 5.1 Data A total of 5 data themes were assembled from secondary sources, including existing maps and aerial photographs of the study area, according to the land qualities required for establishing suitability classes for agriculture. Information was assembled on temperature, water availability, soils, soil salinity, and slope. All data themes were converted into digital form as ARC/INFO coverages. The specific preparation of data on each land quality (table 1) is summarized be. Temperature, t: The mean air temperature at any location in the general region of the Cimanuk watershed is directly related to elevation, decreasing by 6 C for every 1000 meters of incremental height. As all elevations in the watershed are be 1000 meters, air temperature was assumed to be constant at 27 C for all locations. Water availability, w: This theme comprised two characteristics, namely successive dry months and average annual rainfall. The dry-month data were obtained from Oldeman (1971). Rainfall data were obtained in cartographic form from the soil Research Institute of Indonesia (SRI, 1976).

12 508 G B Hall, F Wang, Subaryono Soils, r, /, n: A total of 8 land characteristics on 3 land qualities are grouped under the general category of soils. Included are the land quality of rooting condition, r, with three characteristics rooting depth, soil texture, and drainage class; the land quality nutrient retention, /, comprising ph and CEC; and the land quality nutrient, n, availability comprising the amounts of P 2 0 5, K 2 0, and nitrogen. These data were obtained from soil maps published by the Indonesian Soil Research Institute in Toxicity, x: Salinity data for the study area were derived by linear interpolation of salinity values in nearby areas, reported in Sigalingging (1985). Terrain, s: Information on a single terrain characteristic, namely slope, was extracted from a topographic map of the study area. Contour lines were digitized to construct a triangulated irregular network (TIN) in ARC/INFO GIS software, from which a slope coverage was extracted. 6 Results 6.1 Boolean analysis wetland rice and soybean Current and potential suitability for each crop consistent with, respectively, prevailing and modified land-characteristics and crop growth requirements are presented for 5 areas as examples. The characteristics of the areas are listed in table 4. Areas 69, 75, and 249 have very similar characteristic values, most of which can be rated as and according to table 2. The exception is the values of available P which fall in S3 for both wetland rice and soybean. In all cases for the Boolean analysis, class membership is precise, or 'crisp'. The rules for evaluating suitability are exactly consistent with those specified in section 3. That is, a land area is either a member of a suitability class or it is not, depending upon the match between suitability-class requirements and actual land characteristics. Moreover, the rule is enforced that no land area can be rated higher in current suitability than its most limiting characteristic despite its performance on other characteristics. Hence, areas 69, 75, and 249 cannot be rated higher than S3 without improvements because of the insufficient level of P Inspection of figures 1(a) and 1(b) for current suitability reveals that, indeed, no areas in the watershed can be rated higher than N or S3 for either crop. Class S3 dominates the study area, covering 62% of the watershed in the case of wetland Table 4. Characteristics of the selected areas. Attribute Average annual temperature ( C) Average annual rainfall (mm) Number of dry months Soil drainage class Soil texture Rooting depth (cm) Cation exchange capacity ph Total nitrogen Available P 2 O s Available K 2 0 Salinity (mm hos cm" 1 ) Slope (%) Area number SP CL 125 very high 5.75 medium very high Note: for soil drainage class: SP somewhat poorly drained, P poorly drained, W well drained; for soil texture: CL silty clay, STCL structured clay, LO loam SP CL 125 very high 5.75 medium very high P STCL 125 very high 6.75 medium high W LO 75 high 5.75 very high P CL,LO 125 very high 5.75 very

13 Comparison of Boolean and fuzzy classification methods 509 rice and 76% of the area in the case of soybean. The results for selected areas in table 5 suggest that, in general, current suitability for wetland rice in class S3 can be improved by one class to. In addition, a large part of the overall catchment (160 km 2 ) currently in class N for wetland rice can be improved to class [figure 2(a)]. The major limitations in each case involve lack of nutrient availability (characteristic n) and soil toxicity (x) from salinity, especially in areas to the north of the watershed Figure 1. The Lower Cimanuk watershed area, West Java, Indonesia: current suitability ratings for (a) wetland rice and (b) soybean, by use of Boolean classification. Table 5. Land suitability for wetland rice and soybean selected areas, Boolean classification. Area Area Current Possible Potential number (km 2 ) suitability 3 improvement 15 suitability (a) Wetland rice (b) Soybean S3 S3 S3 N M N S3 rn S3 vj~> rnx S3 r N, ODrn M/MI M/MI M/MI MR/HI M/HI X X X R/HI TM/HI a For symbols of current suitability see table 1. b Symbols relating to soil improvement: T drainage, M fertilizer, R land reclamation, X no improvement possible; other symbols: MI medium input, HI high input. S3 S3 S3

14 510 G B Hall, F Wang, Subaryono located close to the sea. Those deficiencies are improved, respectively, by application of fertilizer (improvement M) and land reclamation of saline soils (improvement R) (table 5). In cases where 3 or more limitations are present in an area no improvement beyond the current suitability class is possible. In the case of soybean, current suitability ratings that fall into class S3 cannot generally be improved because of poor soil texture within land quality r (table 3); although there are exceptions, such as area 399, contingent upon soil type (silty clay loam) and improved drainage. Also, inadequate nutrient availability is a significant problem for this crop, limiting it to a maximum potential suitability rating of S3 in 76% of the study area. It is clear, however, from figure 2(b) that some areas in the south and two smaller coastal areas to the northeast of the catchment improve their current suitability from, respectively, S3 and N to a potential suitability rating of through high inputs of fertilizer, reclamation, and drainage. Individually, these improvements mitigate the limiting effects of nutrient availability (n), toxicity (x), and rooting condition (r). It is clear from figures 1 and 2 that large areas of the catchment fall into a small number of classes in current and potential suitability for each crop. This result is characteristic of Boolean processing where the decision rule for suitability is limiting and precise. Moreover, from the sample results presented in table 5 it is impossible to determine the extent to which, for example, areas 69 and 75 differ in the degree of suitability for wetland rice. Both areas are treated as exactly the same in the classification process (S3, current suitability;, potential suitability) even though localized conditions are likely to vary on all land characteristics. Fuzzy information processing on the same data overcomes such interpretive limitations and offers land-use planners and decisionmakers better insight into degrees of suitability within classes. We demonstrate this in the foling section. Figure 2. The Lower Cimanuk watershed area, West Java, Indonesia: potential suitability ratings for (a) wetland rice and (b) soybean, with use of Boolean classification.

15 Comparison of Boolean and fuzzy classification methods 511 4i!^^^^y^^8BH«lic!iw 1 y:mbe ^My I ' S '^^frbllllllllb Java Sea "* ^ '**WMMl^^Hmmm!P m <" \ 1 iiill 11 jwbii^lllli'i 'i 'i jmk a ^ "-- 11 ^Hi^i^i^i^i^iMBMIIllH. fll ^ ^''lliiilibhb^ l ->* % 1 IB IMMfflM^^ HL,' J ^ - 1 ^^lllliiim^ <u - a ililllh ^^-^-i^-^i^hiii^i^i^a -a " JHmwlMF"^1" 1111 ' ^ 1-5 illlllllw "> ^ JV 1 '"WIBfiliiWWJM imam a - Jf ih^hiilyic^ 1 D )fi ^^KKtNKK^K^^k highly suitable moderately suitable S3 marginally suitable N not suitable (b) Figure 3. The Lower Cimanuk watershed area, West Java, Indonesia: current suitability ratings for (a) wetland rice and (b) soybean, with use of fuzzy classification. T3 ^m Unsurvej area V, Java Sea W^2Li^^^^^ IH?^ W*/;mwmA \ highly suitable moderately suitable S3 marginally suitable N not suitable [Jg t BfcLjl (a; Figure 4. The Lower Cimanuk watershed area, West Java, Indonesia: potential suitability ratings for (a) wetland rice and (b) soybean, with use of fuzzy classification.

16 512 G B Hall, F Wang, Subaryono 6.2 Fuzzy analysis wetland rice and soybean The fuzzy pattern recognition method described earlier was applied to evaluate current and potential suitability for the same crops. To use equation (6) to compute membership grades, the textual symbols in the collected data and class representative vectors were converted into numbers. For example, VL (very ), L (), M (medium), H (high), and VH (very high) were converted into 2, 4, 6, 8, and 10, respectively. The other values were normalized in the range from 0 to 10. Figures 3 and 4 illustrate the spatial extents of current and potential suitability for the two crops. The plotted suitability classes are 'hardened' from fuzzy classification. A 'hardened' map is a visual representation of part of the analysis results the most probable class for each area. The 'hardened' map is derived by assigning to each area the label of the class in which the area has the highest membership grade. The result is quite consistent with conventional analysis but is much more informative, and the information contained in the membership grades is available in the internal representation for subsequent use Current suitability For each crop, an area is associated with 4 membership grades indicating the extents to which the area currently belongs to the 4 suitability classes. Compared with the Boolean suitability classification, which rates an area simply according to its most limiting characteristic, the pattern recognition method takes into consideration all characteristics. Also, compared with the hard partition which assigns a single class to an area, the fuzzy partition provides information about the membership extents of each class Wetland rice As noted above, areas 69, 75, and 249 have similar characteristic values. Viewing the characteristics as whole, the 3 areas can be rated into. This is consistent with the results of the fuzzy pattern recognition methods which generate the highest membership grades in for the 3 areas (table 6). The fuzzy membership grades calculated for each area in each class provide information about land suitability beyond the capability of the Boolean analysis. For example, in the case of wetland rice, the grades indicate that areas 69, 75, and 249 are in intermediate conditions between and. Moreover, the grades reveal the differences between the 3 areas. The major difference between the 3 areas lies in the values of soil salinity. Area 75 has the highest salinity that can be rated in, and has the highest grade of of the three areas. Area 249 has the est salinity that can be rated in. Its grade in is er than area 75 but Table 6. Current suitability from fuzzy analysis for selected areas. Area number (a) Wetland rice (b) Soybean Land-suitability ratings S3 N C Note: C hardened suitability class N N

17 Comparison of Boolean and fuzzy classification methods 513 its grade in is higher. This implies that area 249 is more suitable for wetland rice than area 75. Area 69 has a salinity value between those of areas 75 and 249. Its membership grades indicate that it is more suitable than area 75 but less suitable than area 249 for wetland rice. In cases where the Boolean rating method (which takes the worst-case scenario) has to be used, the fuzzy pattern recognition enables better understanding of land suitability. For example, areas 47 and 399 have very values for P availability which are rated in class N. The other quality values of area 399 are in class to S3, but area 47 has a very high soil salinity which is also in class N. According to the Boolean method, both area 399 and area 47 are rated in the same class N. But actually, area 47 is more unsuitable for wetland rice. The membership grades may help us to understand the difference. If the grade of area 47 in class N implies that the area is 'rather unsuitable', the grade of area 399 may be interpreted as that the area is 'not so unsuitable' Soybean Similar results are obtained for soybean. Most of the characteristics of areas 69, 75, and 249 can be rated in. Thus, the highest membership grades of three areas are in class. This is reasonable when all the characteristics are considered as a whole. The differences in the suitability of the 3 areas for soybean can be understood from their membership grades. Area 249 has the best ph value and est salinity among the three; it has the highest membership grade in Potential suitability Each area is also associated with 4 membership grades indicating the degrees to which it belongs to the suitability classes after limiting land qualities are improved. By comparing the membership grades for current and potential suitability, we can understand the extent to which the suitability of an area can be improved, even though the hardened class of the area remains the same. This enables us to estimate the benefit-cost ratio more accurately before actual improvement effort is made. This is not possible with conventional Boolean analysis Wetland rice The most limiting factor of areas 69, 75, and 249 is the available P which is categorized in land-quality class, ft nutrient availability. The potential suitability of the three areas by improving the availability of P through application of fertilizer is listed in table 7. The hardened suitability class of area 249 can be rated into, one class higher than the current one. Although the hardened potential suitability classes of areas 69 and 75 remain, higher Table 7. Potential suitability, from fuzzy analysis selected areas. Area number F I Land-suitability ratings HPS (a) Wetland rice (b) Soybean n n n nx n rn rnx rn X rn M M M X M M M M R M S3 N Note: F most limiting factor (see table 1 for definition of symbols); I possible improvement (see table 5 for definition); HPS hardened potential suitability. S3

18 514 G B Hall, F Wang, Subaryono membership grades in and indicate that the two areas can become more suitable for wetland rice by improving the availability of P 2 O s. The most limiting factors of area 47 are the availability of P (in quality n) and salinity (in quality x). The most limiting factor of area 399 is the availability of P Table 7 illustrates that by decreasing salinity and increasing P availability through application of fertilizer (M) for areas 47 and 399, respectively, the 2 areas can be upgraded for wetland rice, although the hardened classes remain the same. The membership grades show that the improvement extent of area 399 is much larger than that of area Soybean For areas 69, 75, and 249, the most limiting factors are soil drainage class and soil texture, which are both in the quality group of rooting conditions. Table 7 lists the potential suitability membership grades and the hardened classes of the areas by improving the drainage class. Area 47 goes from S3 to because of toxicity improvement through high levels of reclamation. Although the hardened classes of the other areas remain the same, the increases of membership grades in indicate the improvements in the land quality. 7 Discussion The insights gained into land suitability for wetland rice and soybean with a fuzzyset-based approach are readily apparent, for both current and potential suitability, from the above results. Several points are noteworthy in this regard. First, it is clear that the hardened-feature space fuzzy suitability evaluation is more discriminating than the worst-case scenario, characteristic of Boolean processing. Whereas large tracts of the study area are rated the same in the Boolean results there is greater variation in suitability in the hardened fuzzy representation. This is an expected result with relaxation of the strict set-membership rules associated with Boolean set theory. Second, and of greater significance, is the ability to extract information concerning the degree of land suitability class membership for tracts of land from fuzzy processing. It is clearly of great relevance to land-use planners, especially in areas such as the Cimanuk watershed which are undergoing substantial land-use stress, to be able to optimize the use of scarce land resources. By using only the results of the Boolean analysis presented above, planners and decisionmakers have no way of knowing how highly or moderately suitable an area of land is for a given crop. There is no ability to determine this from the results of Boolean processing, other than perhaps noting the number and type of limitations identified for areas of land within a suitability class. Areas rated as S3, for example, are treated exactly the same irrespective of within-class variations across land characteristics. In contrast to Boolean results, fuzzy processing als decisionmakers to observe, in a straightforward and easily understood manner, the extent to which an area is associated with a suitability class. This is recorded by the membership grades for each class. On this basis, decisionmakers may evaluate land suitability for given crops, not just on simple class membership but on the level of class membership. This als more realistic judgments to be made on land suitability based on all land characteristics. A third advantage of fuzzy suitability evaluation over the Boolean approach is the flexibility of the former. Results can be generated by using the fuzzy pattern recognition method for current and potential suitability for any number of crops individually and in combination. Although this is also possible using Boolean analysis, the membership grades that are vital to informed decisionmaking are retained only in the internal representations oj fuzzy analysis for subsequent use (Wang et al, 1990). Thus the information content of the membership grades is considerably richer than the 'all-or-nothing' information supplied by the Boolean method.

19 Comparison of Boolean and fuzzy classification methods 515 Although the fuzzy analysis methods increase the amount of useful information to the user, they also increase the user's burden in interpreting the analysis results. This can be mitigated by creating a 'grade interpreter' which is able to translate the membership grades into natural language qualifiers, such as 'rather' and 'not so'. When precise quantitative analysis of the membership grades is not required, the grade interpreter may provide for an end user sufficiently informative and easily understood interpretation of membership grades. Such an interpretation can be achieved based on the connection between fuzzy sets and natural languages (Zadeh, 1981). 8 Conclusion In this paper we presented and compared two GIS-based methodologies for the assessment of land suitability for agriculture. Although Boolean analysis was shown to be capable of handling large data sets and complex evaluation criteria, fuzzy analysis was shown not only to be more informative to decisionmakers but also to be more realistic in its ability to handle accurately variation in the levels of all land characteristics considered. The data processing and analysis presented in the paper were undertaken by using ARC/INFO GIS software software. The map overlay was conducted by using the ARC UNION operation. The procedure for determining Boolean membership grades was coded as an INFO database program, and the fuzzy membership grades were calculated by a C program and then incorporated back into the composite coverage attribute table in ARC/INFO. Despite the advantages offered by the fuzzy analysis method, at least two major problems continue to impede GIS applications in spatial analysis in general and land evaluation in particular. The first problem concerns inaccuracies inherent in source data that are compounded as the data themes are sequentially overlaid to produce a working database. Spatial registration of composite information is only as accurate as the combined spatial and other aspects of the source data. As noted earlier, the pattern recognition method used in this paper is much less sensitive to noisy data than the conventional, Boolean method. Further research should be directed toward this issue to understand better the effect of varying degrees of noise on fuzzy and indeed Boolean processing. The use of simulated data sets where the extent of noise can be controlled is a worthwhile prospect to pursue in this area. Second, the process of polygon boundary definition and topological overlay of polygon coverages in all conventional GIS packages are examples of classical set theory that suffer from the limitations of Boolean processing discussed above. Future research must address the relationship between error propagation and problems with polygon boundaries. This is especially true in research that uses polygonized thematic maps as source data for analysis of landscape features, such as soil characteristics, that are in fact continuously distributed. Although some research has been started to address these problems (Huevelink et al, 1989) a great deal of work remains to be done. It is important, as the subject of land evaluation for agriculture and other uses turns increasingly toward GIS, to realize the constraints inherent with Boolean analysis and to develop new approaches. Numerous researchers have noted that most landscape features do not conform to crisp, mutually exclusive classes. The continued representing and processing of landscape features as such in conventional GIS software cannot help but fail to misrepresent reality. Fuzzy set theory als land-evaluation applications tojcnove much closer toward real conditions. By utilizing this concept in data representation and processing, better informed decisions on land use can be made than might otherwise be possible.