Definition of Zones With Different Levels of Productivity Within an Agricultural Field Using Fuzzy Modeling

Zoning of agricultural fields is an important task for utilization of precision farming technology. A method based on fuzzy indicator model theory for definition of zones with different levels of productivity is considered. Fuzzy indicator model for identification of zones with different levels of productivity is based on two general types of fuzzy indicators: the individual fuzzy indicator (IFI) type and the combined fuzzy indicator (CFI) type. IFIs are defined as a number in the range from 0 to 1, which reflect an expert concept and are modeled by an appropriate membership function. CFI is defined using fuzzy aggregated operations. The theoretical considerations are illustrated with this example based on data collected from a precision agriculture study in central Texas, USA. Soil samples were collected at different points, taking into account the actual longitude and latitude for each of these points. Because the experimental data (as in many cases) contained information only about a limited number of parameters, the calculations were restricted in this study. In this study, the parameters grain yield, total carbon (C), total nitrogen (N), and available phosphorus (P) were utilized. Using the author’s computer program, fuzzy indicators IFI/CFI was calculated for each zone separately. Utilizing results of calculations maps of zones with different levels of productivity were built.


Introduction
Within-field variability is a well-known phenomenon in agriculture and is central to the precision farming concept. One way of dealing with this problem is to subdivide a field into a few contiguous homogenous zones, often referred to as management zones (MZs) (Handbook of precision agriculture-principles and applications, 2006). However, decisions must be made as to how these management zones will be delineated. The evaluation of MZs delineation is the subject of many scientific research studies.
The delineation of management zones could be based on factors such as soil and field characteristics (Fridgen, 2000;Fridgen et al., 2004), digital elevation model (Pilesjo et al., 2000) and yield maps (Stafford et al., 1999). Another method is based on the use of GIS software. Yield values are calculated on a cell-by-cell basis and a map of average yield values is created (Mitchell, 1999).
The most developed approach is based on some sort of clustering methods. Clustering using the fuzzy k-means algorithm (fuzzy c-means) was described by Tou and Gonzalez (1974) and Fraisse et al. (1999). Yakushev et al. (2007) discussed a method for recognizing relatively homogeneous zones based on limit theorems of probability theory.
In recent years, some progress in the study of within-field variability has been achieved by application of a fuzzy indicator model (Kurtener et al., 2008;Torbert et al., 2009;Krueger et al., 2010). Using this model, it is possible to achieve agricultural field zoning on the bases of the combination of several soil and crop characteristics. This paper reports on the development of a fuzzy indicator model for definition of zones with different levels of productivity within an agricultural field. The theoretical considerations are illustrated with this example based on data collected from a precision agriculture study in central Texas, USA. The range of parameters within Z 1 1.5 -2.4 0.05 -0.1 0.015 -0.03 6.28 -7.53 The range of parameters within Z 2 2.41 -3.5 0.11 -0.27 0.031 -0.045 7.60 -8.79 In this example, we used the trapezoidal-shaped built-in membership function. This function is characterized by four reference points: x low1 , x opt1 , x opt2 , and x low2 . Mathematically the trapezoidal-shaped built-in membership function is described as follows: For example, reference points for the total carbon in areas with good productivity (Z 2) are: x low1 = 2.3%, x opt1 = 2.5%, x opt2 = 3.4%, and x low2 = 3.6%.
Using the author's computer program, fuzzy indicators IFI/CFI were calculated for each zone separately. For illustration the results of calculations of fuzzy indicator on total carbon (IFI C ) for both zones Z 1 and Z 2 are presented in Table 2.   Vol. 5, No. 5;2013 For example in Figure 5, the map based on values of fuzzy indicator CFI for zone with a medium level of productivity contains only the area within which the presence of the zone is medium (0.2 < CFI < 0.5) and the area within which the zone is weak (0 < CFI < 0.2) practically does not exist.

Conclusion
The backbone of this research is the development of an appropriate method for definition of zones with different levels of productivity within an agricultural field. This method is based on fuzzy indicator model, which could be very useful for analysis of within-field variability. To illustrate the proposed method, a series of calculations were made. As input data we used data from an experiment, conducted on the North agricultural field located in Bell County, TX on the Elm Creek watershed (Torbert et al., 2000).