ISPRS Int. J. Geo-Inf. 2012, 1, 272-293; do:10.3390/jg1030272 Artcle OPEN ACCESS ISPRS Internatonal Journal of Geo-Informaton ISSN 2220-9964 www.mdp.com/journal/jg/ A Spatal Mult-Crtera Model for the Evaluaton of Land Redstrbuton Plans Demetrs Demetrou 1, *, Lnda See 2,3 and John Stllwell 1 1 2 3 School of Geography, Unversty of Leeds, Leeds LS2 9JT, UK; E-Mal: j.c.h.stllwell@leeds.ac.uk Internatonal Insttute of Appled Systems Analyss (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austra; E-Mal: see@asa.ac.at Centre for Advanced Spatal Analyss (CASA), Unversty College London (UCL), London WC1E 6BT, UK; E-Mal: l.see@ucl.ac.uk * Author to whom correspondence should be addressed; E-Mal: demdeme@cytanet.com.cy; Tel.: +357-99-428-462; Fax: +357-25-824-225. Receved: 18 August 2012; n revsed form: 23 October 2012 / Accepted: 26 October 2012 / Publshed: 9 November 2012 Abstract: A plannng support system for land consoldaton has been developed that has, at ts heart, an expert system called LandSpaCES (Land Spatal Consoldaton Expert System) whch contans a desgn module that generates alternatve land redstrbutons under dfferent scenaros and an evaluaton module whch ntegrates GIS wth mult-crtera decson makng for assessng these alternatves. Ths paper ntroduces the structural framework of the latter module whch has been appled usng a case study n Cyprus. Two new ndces are ntroduced: the parcel concentraton coeffcent for measurng the dsperson of parcels; and the landowner satsfacton rate for predctng the acceptance of the land redstrbuton plan by the landowners n terms of the locaton of ther new parcels. These two ndces are used as crtera for the evaluaton of the land redstrbuton alternatves and are transferable to any land consoldaton project. Moreover, a modfed verson of the rato estmaton procedure, referred to as the qualtatve ratng method for assgnng weghts to the evaluaton crtera, s presented, along wth a set of non-lnear value functons for standardzng the performance scores of the alternatves and ncorporatng expert knowledge for fve evaluaton crtera. The applcaton of the module showed that t s a powerful new tool for the evaluaton of alternatve land redstrbuton plans that could be mplemented n other countres after approprate adjustments.
ISPRS Int. J. Geo-Inf. 2012, 1 273 A broader contrbuton has also been made to spatal plannng processes, whch mght follow the methodology and nnovatons presented n ths paper. Keywords: land consoldaton; mult-attrbute decson makng; parcel concentraton coeffcent; landowner satsfacton rate; qualtatve ratng method; value functons; GIS 1. Introducton Land fragmentaton occurs when sngle landholdngs consst of numerous spatally separated land parcels [1]. Land consoldaton s consdered to be the most effectve land management approach for solvng ths problem and s undertaken n many countres around the world [2,3]. Land consoldaton ncludes the process of land reallocaton, whch can tself be dvded nto two sub-processes, land redstrbuton and land parttonng. Land redstrbuton comprses the preparaton of a prelmnary plan to restructure land parcels n terms of ther number, ownershp, sze, value and approxmate locaton based on legslaton, the exstng land tenure structure, rules of thumb and the experence of the planner. For example, n Cyprus, the development of such a plan requres that a team of land consoldaton planners meet wth each land owner n order to understand ther preferences, the most mportant aspect beng where ther new parcels should be located. An acceptable plan, determned from a set of alternatves s then drawn up, whch forms the bass of land parttonng n whch new parcels are created that consoldate the land holdngs and mnmze the amount of spatal separaton between the parcels belongng to each landowner. One problem wth the land consoldaton process s the amount of tme needed to complete each land consoldaton project. For example, the average project duraton s 8 16 years n Germany, 10 12 years n the Netherlands, 8 12 years n Fnland and 5 7 years n Sweden [4]. In Cyprus, a project takes on average from 6 to 10 years [5] wth 2 3 years spent on the preparaton of the land reallocaton plan. The amount of tme requred s partly a functon of the lack of adequate tools to support land consoldaton, snce propretary geographc nformaton systems (GIS) are not capable of handlng the complexty nvolved. Demetrou et al. [6] have proposed a framework for an ntegrated plannng and decson support system (IPDSS) whch encapsulates the entre land reallocaton process nto an automated workflow. Usng ths framework embedded wthn a GIS envronment, the LAnd CONsoldaton Integrated Support System for plannng and decson makng (LACONISS) system was developed, whch conssts of three man sub-systems: a Land Fragmentaton System (LandFragmentS) [7]; a Land Spatal Consoldaton Expert System (LandSpaCES) [8]; and a Land Parcellng System (LandParcelS) [9]. Ths paper s specfcally concerned wth a methodology for evaluaton but we must acknowledge that evaluaton n the context of land consoldaton may have dfferent meanngs accordng to whether t refers to sutablty evaluaton, comprehensve project evaluaton or land reallocaton plan evaluaton. Sutablty evaluaton studes [10 12] are carred out before project mplementaton and am to nvestgate the potental for applyng land consoldaton. Comprehensve evaluaton studes [13 18] are broad based and consder the potental mpacts of the whole project usually n terms of three man components: economc effcency whch s related to the mprovement of land
ISPRS Int. J. Geo-Inf. 2012, 1 274 fragmentaton ndces and the consequent agrcultural benefts (e.g., producton, productvty, farmers ncome); envronmental mpacts; and socal mpacts coverng the potental project mpacts to landowners or a group of people or to socety as a whole. Ths knd of evaluaton can be appled ex-ante or ex-post wth the latter beng the most usual case. The thrd type of evaluaton,.e., land reallocaton plan evaluaton studes [19 22] has a narrow scope, focusng on the qualty of the land reallocaton plan durng the desgn stage,.e., ex-ante evaluaton. However, exstng studes do not present any methodologcal developments n ths area because they use solated ndces regardng land fragmentaton such as the sze, shape and dsperson of parcels and hence they do not provde a systematc method for evaluatng land reallocaton or land redstrbuton plans. One reason may be that land reallocaton plans are usually generated manually, resultng n a sngle (although not necessarly optmal) soluton. Thus, wthn the LACONISS system, the LandSpaCES sub-system conssts of two components. The frst s a desgn module, whch s an expert system (ES) that can generate alternatve land redstrbuton solutons [8] n an automated way. The second s an evaluaton module that ntegrates GIS wth a mult-attrbute decson-makng method (MADM) to evaluate these solutons effcently and systematcally accordng to the specfc needs of each land consoldaton project and to assst n the selecton of an optmum soluton. The purpose of ths paper s to outlne the methodology that we have developed for ths evaluaton process, whch s embedded wthn LandSpaCES and whch ncorporates new concepts such as the parcel concentraton coeffcent (PCC) for characterzng parcel dsperson and the landowner satsfacton rate (LSR) whch attempts to capture the preferences of each landowner n an automated way. The methodology s then demonstrated on a real land consoldaton case study n Cyprus where ten alternatve land redstrbuton solutons have been generated under a set of dfferent scenaros. More detals of the generaton of these alternatve land redstrbuton solutons can be found n Demetrou et al. [8]. 2. Methodology The evaluaton of alternatve land redstrbuton plans uses mult-attrbute decson makng (MADM) methods [23,24] whch attempt to fnd the best soluton among a dscrete number of alternatve solutons. The process s llustrated n Fgure 1 where ntally a set of alternatve land redstrbutons s generated and the planner has to select a set of evaluaton crtera to assess these alternatves. Ths produces an effect table wth the alternatves n columns and the crtera n rows. The performance of each alternatve for each crteron s represented by a score that consttutes an element of the effect table located n a cell of the matrx. The scores are standardzed to values between 0 and 1 (representng worst and best performances of alternatves, respectvely) and weghts are chosen for each crteron by the planner. The decson rules comprse the evaluaton method utlzed n order to rank the alternatves. Fnally, a senstvty analyss s carred out amed at assessng the robustness of the rankng order followed by the output of a fnal recommendaton about the most benefcal soluton. Each component of the process s now explaned n further detal n the sectons that follow. The entre process descrbed above has been embedded n a GIS envronment (.e., ArcGIS) by utlzng VBA and ArcObjects [25,26]. Several authors refer to the ntegraton of mult-crtera methods wth GIS [27 30]. The role of GIS s crtcal n both desgnng and evaluatng the alternatve solutons [8]. In terms of the
ISPRS Int. J. Geo-Inf. 2012, 1 275 latter, GIS automatcally provdes all the metrcs of each alternatve for each of the evaluaton crtera nvolved, a task that would be mpossble to carry out manually or through usng conventonal non-spatal systems snce the spatal component of the problem sgnfcantly ncreases the complexty of the calculatons. Fgure 1. General model of mult-attrbute decson-makng method (MADM) (adapted from Sharf et al. [31]). 2.1. Evaluaton Crtera The selecton of the approprate crtera begns wth the defnton of a herarchcal objectve tree specfed va the goal, ams and objectves of the land consoldaton problem [32]. Thereafter, a specfc land redstrbuton objectve tree can be formulated (Fgure 2) whch contans the ams, objectves and the correspondng crtera/attrbutes, whch can be used n the evaluaton of the alternatve land redstrbuton plans. Whlst Fgure 2 shows nne possble crtera, Demetrou et al. [32] suggest that only the followng fve crtera are requred: the mean sze (as a percentage change before and after applyng a soluton) of the new parcels (C1); the mean parcel concentraton coeffcent (C2); the change (as a percentage) n the number of landowners (C3); the percentage of ownershps completed nvolvng the percentage of ownershps that had less than the mnmum sze lmt provded by legslaton and complete to reach that mnmum lmt (C4); and the mean landowner satsfacton rate (C5). Both the PCC and LSR are new concepts, whch are explaned n more detal below.
ISPRS Int. J. Geo-Inf. 2012, 1 276 Fgure 2. The objectve tree for the land redstrbuton problem. 2.1.1. Parcel Concentraton Coeffcent (PCC) A basc measure of spatal dsperson s standard dstance whch s the spatal equvalent of the standard devaton, showng how locatons or ponts are scattered around the spatal mean [33,34]. The spatal mean or mean center of gravty s an mportant spatal statstcal measure of central tendency whch ndcates the average locaton of a set of ponts defned n a Cartesan coordnate system. Thus, standard dstance measures the degree to whch parcels (or more precsely the centrods of parcels) are concentrated or dspersed around ther geometrc mean. Although, n practce, the dsperson of holdngs s dependent on the locaton of the farmstead or the vllage where the farmer resdes, and n ths case transport dstances could be calculated based on some assumptons [21], the extra nformaton needed s usually not avalable, so the mean center of parcels of a holdng s a proxy crteron that gves an adequate representaton of the dsperson before and after land consoldaton. An extenson of both statstcs s the weghted mean center and the weghted standard dstance where centrods may have dfferent attrbute values representng the dfferent szes or land values of each parcel. For nstance, f the largest parcels of a holdng are very much dspersed n terms of locaton, ths may have greater negatve effects on producton, productvty, labor and hence the ncome of farmer, than f the smaller parcels are dspersed [19]. Thus, the weghted mean center of a holdng s a better ndcator than the smple mean center because t reflects not only the spatal dsperson of parcels but also the agrcultural mportance of each parcel. Expressng these spatal statstcs n the context of land consoldaton, the mean center of the parcels of a holdng can be expressed as: n n x y 1 1 x hmc, y hmc, n n (1)
ISPRS Int. J. Geo-Inf. 2012, 1 277 where x hmc and y hmc are the co-ordnates of the mean center of the holdng; x and y are the co-ordnates of the centrod of parcel ; and n s the number of parcels belongng to a holdng. The weghted mean center of a holdng can be calculated n a smlar way as: n n w x w y 1 1 x whmc, y whmc, n n (2) w w 1 1 where x whmc and y whmc are the co-ordnates of the weghted mean center of the holdng and w s the weght of each parcel. From these quanttes, the dsperson of parcels (DoP) and the weghted verson of DoP can be calculated as: DoP Weghted DoP n n 2 ( x xhmc) 1 1 n ( y y n n 2 w ( x xhwmc) 1 1 n 1 w hmc ) w ( y 2 y hwmc ) 2 (3) (4) where both measures have been utlzed prevously by Tourno et al. [19]. However, the dsadvantage of these measures s that they may vary across an unlmted range of values wth no explct extreme values, whch renders nterpretaton dffcult. In ths research, a new ndcator s developed called the parcel concentraton coeffcent (PCC) for each holdng whch s measured on a scale between 1 and 1. A value of zero ndcates no change n the dsperson of a holdng s parcels before and after land consoldaton. The value of +1 refers to the stuaton of perfect concentraton whle 1 represents the worst concentraton. The DoP can be calculated for each holdng twce,.e., before (DoP b ) and after (DoP a ) land consoldaton and then combned to calculate the PCC for three stuatons: 1. If DoPb DoPa then PCC = 0 and the dsperson of parcels has not changed. In ths stuaton, land consoldaton has not acheved any concentraton of parcels for the holdng concerned ndependently of the number of new parcels allocated to a landowner (n') or the number of orgnal parcels owned by the landowner (n). 2. If DoPb DoPa the PCC can be expressed as: DoPb DoPa DoP b PCC n' In ths stuaton, an mprovement n the dsperson of parcels has occurred. The maxmum value of 1 means that parcels have been concentrated after land consoldaton nto a sngle parcel,.e., n' = 1 and perfect concentraton has been acheved. Ths happens when the DoP a equals 0 and consequently n' = 1. The numerator n Equaton (5) represents the proportonal change of dsperson before and after land consoldaton of a holdng. The denomnator,.e., n', adjusts the proportonal change n dsperson (5)
ISPRS Int. J. Geo-Inf. 2012, 1 278 (the level of concentraton) snce the PCC ncreases as n' decreases. In other words, the hgher n', the less the concentraton of new parcels and hence PCC reduces towards a value of zero. 3. If DoPb DoPa, then the PCC s expressed as: DoPa DoPb DoP a PCC n In ths stuaton, deteroraton n the dsperson of parcels has occurred. Ths may occur when ether n' s greater than n (whch s a very rare case) and/or when the parcels have been allocated at greater dstances. The extreme value of 1 means that the concentraton of parcels after land consoldaton has worsened ndependent of the number of new parcels allocated snce the basc am of concentratng parcels va land consoldaton has completely faled. Ths happens when the DoP b equals 0 and consequently n = 1. The denomnator n adjusts the proportonal change n dsperson,.e., the level of concentraton, snce the PCC ncreases as n ncreases. In other words, the greater the value of n, the less extreme the dfference (before and after a project) n parcel concentraton and hence PCC reduces towards zero because the dsperson was already poor. 2.1.2. Landowner Satsfacton Rate (LSR) The landowner satsfacton rate (LSR) s an ndcator that captures the satsfacton of the landowners wth regard to ther preferences n terms of the locaton of ther new parcels. It s based on the parcel prorty ndex (PPI) ntroduced n Demetrou et al. [8], whch ranks the preferences of the landowners regardng the locatons of the new parcels they wsh to receve. The calculaton of the LSR nvolves determnng whch preferences of each landowner have been satsfed and assgns a proportonal percentage of satsfacton (called the partal satsfacton rate, PSR) to each new parcel dependng on the rankng of the preference satsfed, wth a maxmum of 100%. A crtcal pont n ths process s that the orgnal parcels of a landowner (n), whch are already n preference rankng order, are dvded nto two parts. The frst covers the stuaton up to n' whlst the other part covers the stuaton for the rest of the parcels,.e., from n n'. Thus, f a new parcel falls n the frst part, the PSR wll be 100% but f t falls n the second part, then the PSR s assgned proportonally,.e., reduced, dependng on n and n. Ths can be expressed mathematcally as follows: If n n' then the PSR for each new parcel allocated to a landowner can be calculated as follows: PSR m P (7) where m s a varable that takes nto account the number of parcels orgnally owned by a landowner (n) and the rank order of the preference of each orgnal parcel (RO ), and P s a lnear functon that expresses decreasng satsfacton for each landowner. The two varables, m and P are computed as follows: m n RO 1 (8) s the m value assgned to those new parcels that fall n the frst part of orgnal parcels as explaned earler. In ths case, the parameter RO n Equaton (8) s replaced by the number of new parcels (n') as follows: (6)
ISPRS Int. J. Geo-Inf. 2012, 1 279 Max m ' n n 1 (9) P s a constant percentage for the redstrbuton of each holdng whch s calculated based on the two parts mentoned earler. In partcular, the parcels that belong n the frst part count as one sub-part whlst the parcels that belong n the second part count as a separate sub-part. Thus, P results by dvdng 100% by the total number of sub-parts whch always equals n n'+1. Therefore, P can be computed as: 100 P ' n n 1 (10) Combnng Equatons (8) and (10) yelds: 100 n RO 1 PSR ' (11) n n 1 The total LSR for each landowner j s then calculated as the mean value of the PSR: ' n PSR LSR j ' (12) n 1 Smlarly, the average LSR for the whole land consoldaton area,.e., the whole project, can be calculated as the mean LSR of all landowners (l) who receved property n the plan as follows: LSR l j1 LSR The above assumptons become clearer by utlzng an example for calculatng PSR and LSR. An example s provded n Table 1 whch nvolves a landowner who orgnally had fve parcels (.e., n = 5) and after land consoldaton receves 1, 2 or 3 parcels (.e., n' = 1 to 3). Each cell of the table contans the PSR value for each combnaton of n and n'. Table 1. An example for the calculaton of the partal satsfacton rate. l Number of New Parcels (n') Allocated to the Landowner n 1 2 3 1 maxm P = 5 20 = 100% maxm P = 4 25 = 100% maxm P = 3 33.33 = 100% 2 M2 P =(5 2 + 1) 20 = 80% maxm P= 4 25 = 100% maxm P = 3 33.33 = 100% 3 M3 P = (5 3 + 1) 20 = 60% M3 P = (5 3 +1 ) 25 = 75% maxm P = 3 33.33 = 100% 4 M4 P = (5 4 + 1) 20 = 40% M4 P = (5 4 + 1) 25 = 50% M4 P = (5 4 + 1) 33.33 = 66.66% 5 M5 P = (5 5 + 1) 20 = 20% M5 P = (5 5 + 1) 25 = 25% M5 P = (5 5 + 1) 33.33 = 33.33% For example, f a landowner has been allocated one parcel (.e., frst column) n the same locaton as ts fourth preference (.e., fourth row), then the PSR and hence the LSR (because n' = 1) s 40%. Smlarly, f the landowner has been allocated two parcels (.e., second column), say n the same locaton as the frst (.e., frst row) and fourth preference (.e., fourth row), then the PSR s 100% and 50% for the locaton of the frst parcel and second parcel, respectvely. In ths case, the average LSR s calculated as 75%. j (13)
ISPRS Int. J. Geo-Inf. 2012, 1 280 2.2. Weghtng the Crtera There are several methods avalable to weght the evaluaton crtera ncludng drect rankng; swng weghts; rankng; ratng; parwse comparson; trade off analyss; and qualtatve translaton [23,31,35]. The most popular are the rankng and ratng methods because of ther smplcty. However, there are problems wth assgnng weghts to a fne scale, e.g., to two decmal ponts n the drect rankng method. In addton, other rankng methods (e.g., the rank sum, rank recprocal and rank exponent method) do not provde the potental to rank two or more crtera wth equal mportance, whch s relevant for ths problem. To develop a smple ft-for-purpose method that allows planners to assgn weghts whle overcomng the aforementoned problems, a modfed verson of the rato estmaton procedure has been developed that uses a smlar qualtatve scale as found n par-wse comparson method s hereafter called the qualtatve ratng method. The crtera are classfed nto the followng seven classes of mportance: extremely hgh; very hgh; hgh; ntermedate; moderate; low; and very low, whch are more ntutve to rank than a number or score, and the crtera may have the same mportance usng ths method. Each class has a predefned range of mportance from 0 to 100 as shown n Table 2 but the rate of ncrease n mportance n the lower part of the scale s 10 ponts whlst n the upper part t s double,.e., 20 ponts. Ths represents an mposed weghtng n favor of the hgher classes. Although ths scorng seems arbtrary, n practce ths s realstc snce planners and decson makers tend to gnore the less mportant crtera n the decson-makng process. After selectng the mportance of each crteron, the weghts are standardzed based on the score assgned to each crteron so that the weghts sum to 1. Table 2. The scale of mportance and the relevant scores utlzed by the qualtatve ratng method. Rank Order Scale of Importance Score Classes 1 Extremely hgh 100 2 Very hgh 80 3 Hgh 60 Upper 4 Intermedate 40 Mddle 5 Moderate 30 Lower 6 Low 20 7 Very low 10 Whatever method s employed for assgnng weghts to crtera, the planner needs to be aware that the weghts of the crtera should be algned wth the range of the correspondng performance scores [35,36]. In other words, the larger the range of a performance score for a crteron, the greater the mportance (hence the weght) of that crteron n terms of ts contrbuton n the rankng of alternatves. Ths s known as the range senstvty prncple [37]. 2.3. Standardzaton Process Standardzaton (or normalzaton) s the process of transformng the scores of the evaluaton crtera nto the same scale so that they can be combned and compared. Several standardzaton methods have been developed, whch generally fall nto: lnear scale transformatons [23,31] and
ISPRS Int. J. Geo-Inf. 2012, 1 281 value/utlty functon approaches. Lnear methods (maxmum, nterval and goal standardzaton) are most commonly adopted because of smplcty and a predefned behavor but they have two man dsadvantages. Frst, they assume a lnear assocaton between the orgnal values and the standardzed values when, n practce, ths relatonshp s more complex; and second, they gnore the judgments of the decson makers as they have no nput n the development of the smple lnear standardzaton functons that are commonly used. These lmtatons are overcome by usng value functons, whch encapsulate human judgment n a mathematcal form. These functons translate the performance score of an alternatve for a crteron nto a value score between 0 and 1, representng the degree to whch a certan decson objectve s acheved. A number of methods have been developed for the creaton of value functons. The most common are the mdvalue, Evalue and drect ratng methods [35]. The latter has been utlzed n ths research because of smplcty and flexblty n terms of assgnng values that depend on the crteron concerned. Drect value ratng nvolves the followng fve steps for each crteron: 1. Identfy the mnmum and maxmum values of the crteron whch correspond to values of 0 (worst) and 1 (best), respectvely. In the context of ths research, the mnmum and maxmum values for crtera C1, C3 and C4 were dentfed from 40 year statstcal records provded by the Land Consoldaton Department (LCD) of Cyprus for 74 land consoldaton projects. For crtera C2 and C5, the mnmum values are zero and the maxmum values are 1 and 100%, respectvely. 2. Defne characterstcs of the value functon,.e., monotoncty, shape, etc. 3. Assgn values to selected crteron scores at equal ntervals between the mnmum and maxmum. 4. Ft a mathematcal equaton through these ponts usng approprate software. 5. Valdate the functons as representatons of preference. The values functons for C1 to C5 for the Cyprus case study are presented n Fgure 3(a e) and as Equatons (14 18) respectvely. Fgure 3(a) shows a concave beneft value functon for the mean percentage change n the sze of parcels represented as: V ( x ) x 13.754 0.882x 2.290 x (14) The value functon ncreases sharply from 0 to 0.8 snce the latter value corresponds to 100%, a score consdered by experts as easly achevable, and then gradually ncreases up to the maxmum score of 600% whch s the hghest ever acheved n land consoldaton projects. Fgure 3(b) s another concave beneft value functon for mean PCC: x V ( x ) (15) 0.181 0.975x 0.153x A maxmum score of 1 whch denotes perfect concentraton of parcels whlst a mnmum of 0 means that nothng has changed n terms of the parcel concentraton after land consoldaton. A mean PCC of more than 0.5 (whch corresponds to a value of 0.8 or 80%) s hghly satsfactory for the experts, snce on most occasons, t s not always possble to jon all the parcels of a holdng nto a sngle parcel. 2
ISPRS Int. J. Geo-Inf. 2012, 1 282 Fgure 3. The value functons for the evaluaton crtera. Fgure 3(c) shows a mxed bell-shaped beneft-cost value functon for the percentage change n the number of landowners: 6 4 4 3 2 2 2 3 7.914 10 x 6.368 10 x 1.36110 x 3.208 10 x 1.332 (16) V( x ) 10 The curve ncreases rapdly from 0 to the peak (20%) where ths range ncludes holdngs that are much smaller n sze than the mnmum lmts provded by legslaton. These propertes wll be redstrbuted (by compensaton) to the other landowners ether manly to complete ther property at the mnmum sze or ncrease the sze of other propertes. The rest of the functon then falls steeply from 20% to 40%, whch represents a negatve effect snce a hgh percentage of landless landowners would be generated, wth many not agreeng to leave ther property for compensaton. Fgure 3(d) shows an s-shaped beneft value functon for percentage of ownershps completed: V( x ) (17) 420.714 7.681x 106.064 x x
ISPRS Int. J. Geo-Inf. 2012, 1 283 The convexty n the frst part of the functon (0 to 25%) represents a low satsfacton rate for the objectve. The second lnear secton (25 to 40%) presents a sgnfcant ncrease n satsfacton where many land redstrbuton alternatves are expected to fall. The fnal concave secton (40 to 60%) s the most desrable n terms of alternatve performance but s the most dffcult to acheve. The fnal beneft value functon represents the mean LSR as a convex curve (Fgure 3(e)): V( x ) 3.906 10 9 x 4 Ths functon ncreases slowly from 0 to 60% correspondng to values of 0 to 0.3, respectvely, representng low mportance and then ncreases steeply between 60 to 90%, representng the most sgnfcant part of the functon. Thus, the objectve to maxmze the acceptance of the plan by the landowners s acheved only at hgh values,.e., greater than 80%. 2.4. Rankng the Alternatves 8.62310 7 x 3 6.44110 5 1.16110 3 1.984 10 4 A value functon approach s then utlzed for orderng the alternatve land redstrbutons, whch s the weghted average of the sngle attrbute values: x 2 x (18) V j N 1 w v j (19) where V j s the overall value (or performance score) of the jth alternatve (j = 1 to M), v j s the standardzed value of the score α j of the jth alternatve wth respect to the th crteron/attrbute ( = 1 to N) measured by utlzng an approprate value functon, and w s the normalzed weght for crteron/attrbute such that: N 1 w 1 (20) The alternatve wth the hghest V j s the best alternatve compared wth the other compettve alternatve solutons. It s noted that n contrast to the value functon approach, other popular aggregaton methods that can be utlzed for evaluatng a set of dscrete alternatves nclude outrankng methods that nvolve a parwse comparson between all the alternatves. Chakhar and Mousseau [38] proposed a general framework to ncorporate these methods nto a GIS. 2.5. Senstvty Analyss Senstvty analyss (SA) nvestgates the mpact of changes n the nputs on the decson outcomes. It s a crtcal task for decson-makng processes snce t reveals how relable the fnal decsons are [30]. For MADM, two mportant elements need to be examned: the weghts of the evaluaton crtera and the crteron scores (or performance measures) [23,39]. However, SA s not common practce n spatal mult-crtera decson problems, and where t has been used, only the senstvty of the weghts has been consdered [40].The senstvty of crteron weghts s crucal because the process of assgnng weghts s subjectve and may demonstrate sgnfcant varaton between the decson makers perceptons and preferences. In addton, the avalable methods for defnng the weghts may lead to
ISPRS Int. J. Geo-Inf. 2012, 1 284 dfferent results. Thus, a decson maker can take better decsons f he/she s aware of how crtcal each crteron s. Trantaphyllou [37,41] developed a methodology for ndvdual decson makng, whch calculates the percentage change needed to alter the current weght of each relevant crteron so as to reverse the rankng order of the correspondng par of alternatves for each combnaton of alternatve pars and for each crteron. The percent top crtcal crteron (that may alter the rankng of the best alternatve), the percent any crtcal crteron (that may alter the rankng of any alternatve) and a senstvty coeffcent for each crteron can be calculated. In the case of group decson makng, e.g., n mult-stakeholder partcpatory processes, other methods can be used such as that provded by Jankowsk et al. [42] n ther web-based Choce Modeler system that nvolves extensve senstvty analyss capabltes at three dfferent levels (global, local and spatal). In addton, the standardzaton process of utlzng value functons also nvolves consderable subjectvty, snce the value functons have been defned by experts and the process of assessng them s nherently prone to uncertantes. The percentage change needed to alter the current performance score (of the frst alternatve from the par) so as to reverse the rank order of the correspondng par of alternatves for each combnaton of alternatve pars and for each crteron can be calculated [37,41].From ths, the most crtcal alternatve, the competng alternatve to the best alternatve, and the percentage change n the relevant performance score that wll alter the rankng can be calculated. The above methodology has been ncorporated nto the evaluaton module of LACONISS and s appled n the case study descrbed n the next secton. 3. Case Study The evaluaton methodology has been appled to an actual land consoldaton project that was carred out n the dstrct of Paphos, whch was amongst the frst land consoldaton projects undertaken n Cyprus. The vllage admnstratve boundares cover a total area of 492 ha of lowland whle the extent of the consoldated area covered 195 hectares. The data for ths land consoldaton project were dgtzed; more detals can be found n Demetrou et al. [8]. The system was appled wth ten dfferent sets of nput facts generatng ten alternatve land redstrbutons. These facts represent eleven decson varables: the mnmum parcel area lmt (n m 2 ) for the land consoldaton area as set by legslaton (F1); the mnmum sze lmt (n m 2 ) of the holdng for a landowner to receve a parcel n the new plan as set by the Commttee (F2); the mnmum land value lmt (n monetary values) of the holdng for a landowner to receve a parcel n the new plan as set by the Commttee (F3); the lower lmt (n m 2 ) of a small holdng sze (F4); the upper lmt (n m 2 ) of a small holdng sze (F5); the lower lmt (n m 2 ) of a medum holdng sze (F6); the upper lmt (n m 2 ) of a medum holdng sze (F7); the lower lmt (n m 2 ) of a large holdng sze (F8); the weght attached to the parcel area for the calculaton of the parcel prorty ndex(ppi ) (F9); the weght attached to the parcel land value for the calculaton of the PPI (F10); and the mnmum resdual area lmt (n m 2 ) for the creaton of a new parcel for those landowners who receve more than one parcel (F11). Each alternatve s descrbed brefly n Table 3 by comparng the facts wth those of alternatve 1,.e., the soluton gven by the experts.
ISPRS Int. J. Geo-Inf. 2012, 1 285 Table 3. The descrpton of the ten alternatve land redstrbutons. Alternatve A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 Descrpton Experts soluton (Irrgated project) Medum area and land value mnmum lmts Hgh area and land value mnmum lmts Unequal PPI weghts for area and land value Low small-medum-large holdngs szes Hgh mnmum area of new parcels wth hgh area and land value mnmum lmts Low mnmum area of new parcels wth hgh area and land value mnmum lmts Low area and land value mnmum lmts wth low small-medum-large holdngs szes Inverse unequal PPI weghts for area and land value (comparng to alt-4) Ard project These alternatve solutons were evaluated based on two dfferent scenaros. Scenaro I nvolves changng the weghts of the crtera based on four dfferent cases whle Scenaro II focuses on dfferent project objectves under two dfferent stuatons. 3.1. Evaluatng Alternatves: Scenaro I 3.1.1. Rankng Alternatves Rankng alternatves s carred out usng four cases. In case 1, all fve crtera have the same weght. In case 2, the weghts were assgned to each of the fve crtera n the followng descendng order of mportance: extremely hgh, very hgh, hgh, ntermedate and moderate. In contrast, the weghts n case 3 were assgned n ascendng order of mportance, whlst n case 4, they were assgned based on the judgment of the prncpal author as: extremely hgh, hgh, hgh, ntermedate and very hgh, respectvely. The performance score and the rank order of each alternatve for each case are shown n Table 4 and a graphcal representaton s provded n Fgure 4. A number of nterestng fndngs can be reported. For example, no one alternatve was found to be the best n all cases. In partcular, alternatves 3 and 10 are ranked as best n cases 1, 3 and 2, 4 respectvely. However, alternatve 3 presents a more stable behavor n all cases than alternatve 10, because the former ranked second n both cases n whch the latter ranked frst. In contrast, alternatve 10 nvolves a hgh unrelablty because t s the only alternatve that presents so much dstance n rankng postons (.e., frst, sxth and nnth) whle all the other alternatves change at worst by two postons n terms of rankng. As a result, alternatve 3 s classfed as the best alternatve. Alteratve 3 also acheves a better balance n terms of performance scores.e., a trade-off between all crtera. Regardless t performs best only n C3 whlst alternatve 10 acheves the hghest performance scores n crtera C1 and C2 and the worst n C3 and C5 n all four all cases (Fgure 5). The varablty of the performance scores of the best and worst alternatves appears to vary greatly per case,.e., 21.4%, 29.8%, 16.1% and 23.2% respectvely, whch means that dfferent facts and dfferent weght schemes may produce consderably varyng alternatves. Furthermore, the rankng of alternatve 1 (that represents the soluton gven by human experts n the case study),.e., ffth or sxth
ISPRS Int. J. Geo-Inf. 2012, 1 286 n the four cases, ndcates that t underperforms compared to alternatves 2, 3, 4 and 9 wth whch t s comparable n terms of facts. Ths proves that the system may produce better solutons than the experts. Moreover, t s clear that alternatve eght ranks last n all cases. A general fndng s that the rankng of alternatves s very senstve to the alteraton of the weghts of the crtera, whch has also been found by Janssen and Retveld [13]. Therefore, planners should be aware both of the weghts assgned to each crteron and hence the weghtng method utlzed. Table 4. The performance score and the rankng order of each alternatve for four weghtng scenaros. Case 1 Case 2 Case 3 Case 4 Rankng Alternatve Score Alternatve Score Alternatve Score Alternatve Score 1 A3 0.823 A10 0.791 A3 0.875 A10 0.797 2 A2 0.820 A3 0.765 A2 0.873 A3 0.789 3 A4 0.809 A2 0.761 A9 0.863 A2 0.784 4 A9 0.809 A4 0.751 A4 0.863 A4 0.775 5 A1 0.808 A9 0.749 A1 0.862 A9 0.774 6 A10 0.804 A1 0.749 A5 0.839 A1 0.773 7 A5 0.787 A5 0.729 A7 0.818 A5 0.750 8 A6 0.737 A6 0.652 A6 0.816 A6 0.695 9 A7 0.735 A7 0.646 A10 0.815 A7 0.690 10 A8 0.647 A8 0.555 A8 0.734 A8 0.612 Fgure 4. Rankng of alternatves for four dfferent crtera weghtng cases.
ISPRS Int. J. Geo-Inf. 2012, 1 287 Fgure 5. Performance of alternatves for all crtera n four cases. 3.1.2. Senstvty Analyss Table 5 and Fgure 6 show the senstvty coeffcent varablty for all crtera for each case; the hgher the senstvty coeffcent, the more senstve s that crteron n terms of changng the rank of the best alternatve or any par of alternatves. It s apparent that all the crtera are very senstve n case 3. The reason s that the weghtng scheme n case 3 can be consdered as a paradox n terms of the mportance of crtera that would normally be assgned by land consoldaton experts because the frst two and the last two crtera have a sgnfcant dstance n terms of weghtng class. As a result, a slght change n the weghts towards a more reasonable scheme causes a change n the rank order of the alternatves. In contrast, the crtera are much less senstve for the other three cases because they nvolve a sensble weghtng pattern n terms of practce. Table 5. Senstvty coeffcent and weght for crtera for the four cases. Crtera Case 1 Case 2 Case 3 Case 4 SensC Weght SensC Weght SensC Weght SensC Weght C1 0.081 0.200 0.025 0.323 0.382 0.097 0.068 0.294 C2 0.028 0.200 0.006 0.258 0.241 0.129 0.016 0.176 C3 0.077 0.200 0.018 0.194 0.096 0.194 0.024 0.176 C4 0.068 0.200 0.010 0.129 0.196 0.258 0.024 0.118 C5 0.032 0.200 0.035 0.097 0.341 0.323 0.026 0.235
ISPRS Int. J. Geo-Inf. 2012, 1 288 Fgure 6. Varablty of the senstvty coeffcent for each crteron for four cases. Table 6 shows the most crtcal crtera and the alternatves. The percent top crtcal crteron (PTCC) s C1 for cases 1, 2 and 4. That s, f the weght for C1 changes by 55.8%, 46.2% and 14.7%, the rankng of best alternatves wll alter,.e., alternatves 3, 10 and 4 for the relevant cases wll change. It s noted that the qualtatve ratng method nvolves a change of 90% from best (.e., extremely hgh mportance) to worst (.e., very low mportance) (Table 2). Hence t s not mpossble to have ths magntude n the percentage changes mentoned earler. Crteron C1 s the most crtcal for three out of four cases snce t presents the hghest range of values for the former and a low range of values for the latter case. Smlarly, the percent any crtcal crteron (PACT) s C1 for cases 1, 3 and 4, and f the weghts of C1 change by 12.3%, 2.6% and 14.7% respectvely, then any rankng may change. Table 6. Crtcal crtera and alternatves for each scenaro. Case 1 Case 2 Case 3 Case 4 Percent top crtcal crteron C1 C1 C4 C1 Percent any crtcal crteron C1 C5 C1 C1 Most crtcal alternatve A9 A9 A4 A1 In addton, the most senstve alternatve n terms of changng rankng s alternatve 9 (because of C4 and C1, respectvely) for cases 1 and 2, alternatve 4 (because of C5) for case 3, and alternatve 1 (because of C5) for case 4. Another nterestng fndng extracted from Table 5 s that there s no assocaton between the senstvty coeffcent and the weghts for each crteron for the three frst cases snce the correlaton coeffcent (R) was calculated as 0, 0.24, 0.09, respectvely. However, there s a relatonshp (R = 0.79) n case 4 perhaps because ths case nvolves weghts assgned by the expert and they have not been randomly defned as n the frst three cases. In addton, the most crtcal crteron s that wth the hghest weght, a result that confrms the fndng of Trantaphyllou [37].
ISPRS Int. J. Geo-Inf. 2012, 1 289 3.2. Evaluatng Alternatves: Scenaro II For Scenaro II, the rankng of alternatves s carred out usng two cases. In case 1, the objectve of the project focuses only on mnmzng land fragmentaton,.e., only two crtera (C1 and C2) are nvolved n the evaluaton. In case 2, only C3, C4 and C5 are nvolved n the evaluaton, whch represent the objectve mnmzng socal mpacts. The rankng of alternatves for each case s shown n Table 7. From ths table and Fgure 7, t can be seen that alternatve 10 s ranked frst n case 1 whle alternatve 3 s ranked best n case 2. In other words, alternatve 10 s best n terms of mnmzng land fragmentaton but worst at mnmzng socal mpacts. In contrast, alternatve 3 s best at mnmzng socal mpacts but s also ranked second n case 1,.e., mnmzng land fragmentaton, revealng agan stablty n performance. Ths clearly llustrates that the objectves of a project play a crucal role n the rankng order n addton to the weght of the crtera. Table 7. The performance score and the rankng order of each alternatve for the two scenaros. Scenaro 1 Scenaro 2 Rankng Alternatve Score Alternatve Score 1 A10 0.750 A3 0.951 2 A3 0.631 A2 0.950 3 A2 0.625 A9 0.934 4 A4 0.624 A1 0.933 5 A1 0.621 A4 0.933 6 A9 0.620 A5 0.916 7 A5 0.593 A6 0.913 8 A6 0.472 A7 0.912 9 A7 0.471 A8 0.843 10 A8 0.352 A10 0.839 Fgure 7. Rankng of alternatves for the two cases. Once agan the varablty of performance scores of alternatves ranked best and worst for case 1 s extremely hgh (53.1%) but t s low for case 2 (11.8%). Ths ndcates that the nput facts n the desgn module strongly nfluence the outcome solutons regardng mnmzng land fragmentaton and, n contrast, only slghtly nfluence the outcomes regardng mnmzng socal mpacts. As a result, ths fndng suggests flexblty for the planner n the former case and lmtatons for the planner n the latter case because of the strct provsons n the legslaton.
ISPRS Int. J. Geo-Inf. 2012, 1 290 The senstvty analyss shows that the most senstve crtera are those assocated wth case 2 (Fgure 8). In partcular, the crtera for case 2 are more senstve than those of case 1 regardless of the hgher varablty of the values n the former case. Ths s a controversal fndng compared wth that for scenaro I. Ths fndng reveals that the selecton of the crtera nvolved n the evaluaton process, and hence the objectves of a project, play a crucal role n the rankng n addton to the weght of the crtera. Fgure 8. Varablty of the senstvty coeffcent for each crteron for the two cases. Based on the prevous analyses, the best soluton s alternatve 3 for both scenaros because t presents the most stable behavor n terms of rank order. Thus, planners would defntely make a decson to mplement ths soluton. The outcome of ths evaluaton,.e., the best soluton, s now passed onto the land parttonng module (LandParcelS) for the automatc generaton of the new parcels n terms of shape, sze, land value and locaton. Ths s the functon of the last module of LACONISS (see [9] for more detals). 4. Conclusons Ths paper has presented a GIS-based methodology for evaluatng alternatve land redstrbuton solutons that s embedded as an evaluaton module wthn LACONISS. The methodology was then demonstrated usng a case study of an actual land consoldaton project n Cyprus. The evaluaton module represents a powerful new tool for the comprehensve evaluaton of alternatve land redstrbuton plans. In addton, two new measures were ntroduced: the parcel concentraton coeffcent for measurng the dsperson of parcels, and the landowner satsfacton rate for predctng the acceptance of the land redstrbuton plan by the landowners n terms of the locaton of the newly allocated parcels. These ndces have general and practcal applcablty that could be transferred to any land consoldaton project. Moreover, a new approach, referred to as the qualtatve ratng method, was presented, whch captures a more realstc way to assgn weghts to the evaluaton crtera. Fnally, a set of non-lnear value functons for standardzng the performance scores of the alternatves for fve evaluaton crtera were developed, demonstratng how expert knowledge s encapsulated n the evaluaton process. The man contrbuton of ths work n the area of land consoldaton s that the evaluaton module presented can also be appled n other countres that mplement land consoldaton projects after approprate adjustments. A broader contrbuton has also been made to spatal plannng processes, whch mght follow the methodology presented n ths paper. In addton, the dsperson
ISPRS Int. J. Geo-Inf. 2012, 1 291 metrc could be adopted by other spatal dscplnes (e.g., n ecosystem analyss) that deal wth the study of the dsperson of pont enttes between an exstng and a new status due to a course of acton. Fnally, the paper has demonstrated that the role of GIS n spatal decson makng s crtcal not only for formulatng alternatve solutons for the problem concerned but also for evaluatng these solutons through embeddng tools such as MADM. The role of the planner n nvestgatng and evaluatng the varous alternatves s facltated so as to reach the optmum decson for mplementaton. References 1. Kng, R.; Burton, S. Land fragmentaton: Notes on a fundamental rural spatal problem. Prog. Hum. Geogr. 1982, 6, 475 494. 2. FAO. The Desgn of Land Consoldaton Plot Projects n Central and Eastern Europe; FAO-Land Tenure Studes: Rome, Italy, 2003. 3. FAO. Opportuntes to Manstream Land Consoldaton n Rural Development Programmes of the European Unon; FAO-Land Tenure Polcy Seres: Rome, Italy, 2008. 4. Vtkanen, A. An overvew of land consoldaton n Europe. Nordc J. Surv. Real Estate Res. 2004, 1, 25 43. 5. Demetrou, D.; Stllwell, J.; See, L. Land consoldaton n Cyprus: Why s an ntegrated plannng and decson support system requred? Land Use Polcy 2012, 29, 131 142. 6. Demetrou, D.; Stllwell, J.; See, L. An ntegrated plannng and decson support system (IPDSS) for land consoldaton: Theoretcal framework and applcaton of the land redstrbuton modules. Envron. Plan. B-Plan. Desgn 2012, 39, 609 628. 7. Demetrou, D.; Stllwell, J.; See, L. A new methodology for measurng land fragmentaton. Comput. Envron. Urban Syst. 2012, submtted. 8. Demetrou, D.; Stllwell, J.; See, L. LandSpaCES: A Spatal Expert System for Land Consoldaton. In Advancng Geonformaton Scence for a Changng World; Geertman, S., Renhardt, W., Toppen, F., Eds.; Sprnger-Verlag: Berln/Hedelberg, Germany, 2011; pp. 249 274. 9. Demetrou, D.; Stllwell, J.; See, L. LandParcelS: A Module for Automated Land Parttonng. Avalable onlne: http://www.geog.leeds.ac.uk/fleadmn/downloads/school/research/wpapers/ 12 02.pdf (accessed on 25 Aprl 2012). 10. Mranda, D.; Crecente, R. Sutablty Model for Land Consoldaton Projects: A Case Study n Galca, Span. In Proceedngs of the Symposum on Modern Land Consoldaton, Clermont-Ferrand, France, 10 11 September 2004. 11. Zou, X.; Luo, M.; Su, W.; L, D.; Jang, Y.; Ju, Z.; Wang, J. Spatal decson support system for the potental evaluaton of land consoldaton projects. WSEAS Trans. Comput. 2008, 7, 887 898. 12. Thapa, G.; Nroula, G. Alternatve optons of land consoldaton n the mountans of Nepal: An analyss based on stakeholders opnons. Land Use Polcy 2008, 25, 338 350. 13. Janssen, R.; Retveld, P. Multcrtera evaluaton of land reallotment plans: A case study. Envron. Plan. A 1985, 17, 1653 1668. 14. Huylenbroeck, G.; Coelho, J.; Pnto P. Evaluaton of land consoldaton projects (LCPs): A multdscplnary approach. J. Rural Stud. 1996, 12, 297 310.
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