USING ORDERED WEIGHT AVERAGING (OWA) FOR MULTICRITERIA SOIL FERTILITY EVALUATION BY GIS (CASE STUDY: SOUTHEAST IRAN)

The Multicriteria Decision Analysis (MCDA) and Geographical Information Systems (GIS) are used to provide accurate information on Pedogenic processes and facilitate the work of decision makers. So, MCDA and GIS, can provide a wide range of decision strategies or scenarios in some procedures. One 15 of the popular algorithm of multicriteria analysis is Ordered Weighted Averaging (OWA). The OWA procedure depends on some parameters, which can be specified by means of fuzzy. The aim of this study is to take the advantage of the incorporation of fuzzy into GIS-based soil fertility analysis by OWA in west Shiraz, Fars province, Iran. For the determination of soil fertility maps, OWA parameters such as potassium (K), phosphor (P), copper (Cu), iron (Fe), manganese (Mn), organic 20 carbon (OC) and zinc (Zn) were used. After generated interpolation maps with Inverse Distance Weighted (IDW), fuzzy maps for each parameter were generated by the membership functions. Finally, with OWA six maps for fertility with different risk level were made. The results show that with decreasing risk (no trade-off), almost all of the parts of the study area were not suitable for soil fertility. While increasing risk, more area was suitable in terms of soil fertility in the study area. So using OWA 25 can generate many maps with different risk levels that lead to different management due to the different financial conditions of farmers.


Introduction
Spatial planning involves decision-making techniques that are associated with techniques such as Multi 30 Criteria Decision Analysis (MCDA) and multicriteria Evaluation (MCE). Combining GIS with MCDA methods creates a powerful tool for spatial planning (Malczewski, 1999;Shumilov et  Multicriteria evaluation may be used to develop and evaluate alternative plans that may facilitate compromise among interested parties (Malczewski, 1996). In general, the GIS-based soil fertility 35 analysis assumes that a given study area is subdivided into a set of basic units of observation such as  (Yager, 1988). Conventional OWA can utilizes the qualitative statements in the form of fuzzy quantifiers (Yager, 1988(Yager, , 1996. The main goal of this paper is to produce the land suitability 45 maps according to OWA operators for GIS-based multicriteria evaluation procedures. OWA has been developed as a popularization of multicriteria combination by Yager (1988 showed that OWA is a multicriteria evaluation procedure (or combination operator). The quantifierguided OWA procedure is illustrated using land-use suitability analysis in Shavur plain, Iran. 55 Liu and Malczewski (2013) used GIS-Based Local Ordered Weighted Averaging in London, Ontario. In the study area, the aim was to implement local form of OWA. The local model was based on the range sensitivity principle. The results showed that there were substantial differences between the spatial patterns generated by the global and local OWA methods.
Accordingly, the study area is one of the most important centers of agriculture in Iran, and the aim of 60 the study is the determination of produce the soil fertility maps according to OWA operators for GISbased multicriteria evaluation procedures in southeast Iran using OWA. In the study, we expected that the selected OWA method is the best method for the determination of multicriteria soil fertility. According to OWA method the amount of soil fertility with different risk levels was determined that is useful for farmers with different financial conditions. 65

Methods
In order to prepare soil fertility maps using OWA method, 45 sample soils were used that after the creation of the interpolation maps for each parameters using Inverse Distance Weighted (IDW) and the creation of a fuzzy parameter map for each parameter, in order to make different risk levels OWA was 70 used. The description of each method is in the following:

Inverse Distance Weighted (IDW)
IDW model was used for interpolating Effective data in determining of soil fertility such as potassium (K), phosphor (P), copper (Cu), iron (Fe), manganese (Mn), organic carbon (OC) and zinc (Zn). IDW interpolation explicitly implements the assumption that things that are close to one another are more 75 alike than those that are farther apart. To predict a value for any unmeasured location, IDW will use the measured values surrounding the prediction location. Assumes value of an attribute z at any unsampled point is a distance-weighted average of sampled points lying within a defined neighborhood around that unsampled point. Essentially it is a weighted moving average (Burrough, et al., 1998): Where x0 is the estimation point and xi are the data points within a chosen neighborhood. The weights (r) are related to distance by dij.
where zi1 ≥ zi2 ≥ . . . ≥ zin is the sequence obtained by reordering the attribute values ai1, ai2, . . ., ain, and 95 uj is the criterion weight reordered according to the attribute value, zij. It is important to point to the difference between the two types of weights (the criterion weights and the order weights). The criterion  (Table 1) (Malczewski, 2006

Case study 115
This study was carried out in west Shiraz, Fars province, Iran. It is an area of about 100.02 km 2 , and is located at longitude of N 29° 31΄-29° 38΄and latitude of E 52° 49΄ to 52° 57΄ (

8
The assessment of soil fertility for agricultural production in the region is vital, which should consider 125 environmental factors and human conditions (Soufi, 2004). In order to predict the variability of soil fertility, P, K, Cu, Fe, Mn, OC and Zn maps were prepared ( Table 2) (Organization of Agriculture Jahad Fars province).

Inverse Distance Weighted (IDW)
In the study area for the determination of soil fertility 45 sample points were used. This data was 135 prepared by the Organization of Agriculture Jahad Fars province in 2012. In the study spline, inverse distance weighted (IDW) and simple krining method (gaussian, circular, spherical, exponential model) were used for the production of raster maps for each soil parameter in ArcGIS 10.2. The results of rootmean-square deviation (RMSE) for three models showed that IDW method (circular model) with lowest RMSE is the best model for the prediction of soil parameters. According to Figure 2 sample 140 points was selected randomly in the study area. In the study area the IDW interpolation was used for produces in order to predict of K, P, Cu, Fe, Mn, OC and Zn that are shown in Figure 3. According to

Fuzzy method
In this study, P, K, Cu, Fe, Mn, OC and Zn maps from IDW were used as input to fuzzy inference 150 system. In order to homogenize each parameter for weightedness by OWA method for preparing the final soil fertility fuzzy method was used. According to FAO (1983) membership function for each were not suitable for fertility (critical limit=). According to the fuzzy map of K parts of north, southeast and west were not suitable (critical limit=). Also parts of north, northwest and south of the study area were not suitable for Cu. Finally it was determined that only parts of northeast, southeast and the small parts of west and east were suitable for soil fertility.

170
Finally to overt each parameter and to prepare the soil fertility OWA method was used. OWA offers a wealth of possible solutions for our residential developmental problems. In our application, seven order weights were applied corresponding to the seven factors that were rank-ordered for each parameter after the modified factor weights were applied. Table 3 Table 3)   Given the standardized criterion maps and corresponding criterion weights, we apply the OWA 185 operator using Eq. (2) for selected values of fuzzy quantifiers: at least one, at least a few, a few, identity, most, almost all, and all are used. Each quantifier is associated with a set of order weights that are calculated according to Eq. (2). Figure 6 shows the six alternative soil fertility patterns.  Figure 6. Soil fertility maps of OWA results for selected fuzzy linguistic quantifiers According to Figure 6 (1) the parts of the study area had high value for soil fertility (high risk level for 190 farmers with good financial conditions). According to Figure 6 (2), with decreasing risk (no trade-off), the area with high soil fertility was determined. So, only the parts of west and southwest of the study area were suitable for soil fertility. While almost all of the parts were not suitable for soil fertility.
According to Figure 6 (3) almost all of the study area had low soil fertility. The Figure 6 (4) showed low risk with average trade-off that in comparison of Figure 6 (2) had more risk. The Figure 6   Based on Table 4, the OWA map was classified in eight classes that is shown in Figure 7 and Table 5.
The results in the study are similar to another research by Mokarram and Aminzadeh (2010), in that they used seven order weights for land suitability. The newest research for different agricultural issues such as soil fertility is by Khaki  research only medium risk (AHP) was used and the researchers did not check different risk levels. In the total, it is stated that using OWA method with difference risk levels can create several maps that can help a user (for example farmer) to make different decisions, according to different financial situations and different risk levels. For example with low risk, the farmer can select an area that has more soil fertility to yield maximum produce. So OWA can be applied for fields of natural science to make 215 accurate decisions.

Conclusions
It has been tried to show the benefits of the fuzzy approach to GIS-based multicriteria analysis. This is especially true in situations involving a large number of criterion maps. The OWA approach provides a mechanism for guiding the decision maker/analyst through the multicriteria combination procedures.
OWA method is an important tool in the management sciences and operational researches. Types of 225 decision rules with definitions in OWA method lead to solve semi-structured decision problems.       Table 3) 340