2.2.1 Fuzzy inference systems

In many practical systems, relevant information comes from two sources: human experts, who describe their knowledge about the system in natural languages, and sensory measures and mathematical models proposed according to physical laws. An important task, therefore, is to combine these two types of information into systems designs [45].

The fuzzy inference system consists of a fuzzification interface, a rule base, a database, a decision-making unit or inference unit, and finally a defuzzification interface. The functional blocks are shown in Figure 4.

The function of each block is:


Based on natural language, a fuzzy logic system is simple to understand and enables the representation and processing of human knowledge in a computer. The inputs, outputs, and fuzzy logic rules are easy to modify. These fuzzy logic features make it particularly well suited for use in a decision support system and is able to assist in the construction of vague rate-based irrigation control maps based on results of an imaging system in real time or by prescriptive maps based on the soil-plant-atmosphere transfer.

Figure 4. Fuzzy inference system. Source: Adapted from Ross [46].

In other words, while decision making in classical theory would be like Eq. (1),

Structure of a central pivot. (a) Basic components, and (b) irrigated land. Source: Adapted from [38].

Irrigation - Water Productivity and Operation, Sustainability and Climate Change

1 if, and only if, x∈ A 0 if, and only if, x∉ A

0≤ μð Þ x ≤ 1 if x partial membership to A

The most evident characteristic of fuzzy logic is to consider that between two values (zero and one) there may be intermediate values, and these values are

(1)

(2)

fuzzy logic would be like Eq. (2) [43].

Figure 3.

32

f xð Þ¼

f xð Þ¼

8 ><

>:

(

1 if, and only if, x∈ A 0 if, and only if, x∉ A

#### 2.2.2 Mamdani inference method

Developed by Mamdani [47], the inference method is the most common in practice and literature. To begin the general view of this idea, it is considered a simple system of two rules, where each rule comprises two antecedents and one consequent. The graphic procedures herein illustrated can be easily extended and maintained for fuzzy rule bases or fuzzy systems with any number of antecedents and consequents. Two different cases of two-input Mamdani systems are considered, where the inputs to the system are scalar values and a max-min inference method is used. Thus, the Mamdani inference method for a set of conjunctive rules for rth rules are given by Eq. (3):

$$\text{if } \propto\_1 \text{ is } A\_1^k \text{ and } \propto\_2 \text{ is } A\_2^k \text{ then } y^k \text{ is } B^k \text{ for} k=1,2,...,r\tag{3}$$

if x is A and y is B then z is z ¼ f xð Þ ; y (4)

Usually, f (x, y) is a polynomial function at the x and y inputs, but it can be any general function as long as it describes the output of the system within the fuzzy region specified in the antecedent of the rule to which it is applied. When f xð Þ ; y is a constant, the inference system is called a zero-order Sugeno model, which is a special case of the Mamdani system, in which the consequent of each rule is specified as a singleton fuzzy [50]. Each rule, in Sugeno model has an output given by a function. Due to this, the result is obtained through a weighted average, thus avoiding the time spent with the defuzzification process necessary in the Mamdani

Integrating Remote Sensing Data into Fuzzy Control System for Variable Rate Irrigation Estimates

Remote sensing technologies are being used more and more often in the precision agricultural applications. This is because that the variables (crop stress, soil type, disease,) to be measured and controlled are very disperse in remote areas with limited wireless communications or no power supply. Also, the measurements of each variable at spatial and temporal scale are expensive and time-consuming for installing and maintaining sensors over each field. Sensors can be multispectral cameras on Satellites or mounted on Unmanned Aerial Vehicle (UAV, or "drones"). In this chapter, we focalized on the using of satellites images for agricultural

Remote sensing imagery can be used for mapping soil properties, classification of crop species (land use), detection of crop water stress, monitoring of irrigation, and predicting of crop yield. The use of remote sensing in precision agriculture depends principally on the spatial, temporal, radiometric and spectral resolution. Satellite remote sensing has shown a very strong potential for irrigation management at large scale through using a different data (optical, thermal and radar)

Optical reflectances in red and near infrared (0.4–12.5 μm) have the potential to

access the vegetation indices (VI) that are directly related the different crop parameters like crop coefficient (Kc) used in estimating the crop water requirements. Several studies (e.g., [51–59]) have been specifically dedicated for

Graphic interpretation of the Sugeno method. Source: Adapted from [50].

model. Figure 6 illustrates the concept of the TSK model.

DOI: http://dx.doi.org/10.5772/intechopen.87023

2.3 Remote sensing

applications.

Figure 6.

35

acquired from different satellites.

This equation has a very simple graphical interpretation, exemplified in Figure 5, and illustrates graphical analysis of two rules, where symbols A11 and A12 refer to the first and second fuzzy antecedents of the first rule, respectively, and symbol B1 refers to the consequent fuzzy of the first rule. The symbols A21 and A22 refer to the first and second fuzzy antecedents, respectively, of the second rule, and the symbol B2 refers to the consequent fuzzy of the second rule.

#### 2.2.3 Takagi-Sugeno-Kang inference method (TSK)

Although originally proposed by Takagi and Sugeno [48], this method is also known in the literature as Takagi-Sugeno-Kang (TSK) model. This is due to the subsequent works by Sugeno and Kang [49] related to methodologies developed to identify this type of model. The fuzzy TSK model consists of an inference system capable of describing, in an exact or approximate way, non-linear dynamic systems through a set of linear, locally valid dynamic systems, smoothly interpolated, nonlinear and convex. A typical rule in a Sugeno model, which has two inputs, x and y, and one output z, is in the form of Eq. (4).

Figure 5. Interpretation of the Mamdani method. Source: Adapted from Ross [46].

Integrating Remote Sensing Data into Fuzzy Control System for Variable Rate Irrigation Estimates DOI: http://dx.doi.org/10.5772/intechopen.87023

$$\text{if } \propto \text{ is A and } \text{y is B then } \text{z is } z = f(\propto, \text{y}) \tag{4}$$

Usually, f (x, y) is a polynomial function at the x and y inputs, but it can be any general function as long as it describes the output of the system within the fuzzy region specified in the antecedent of the rule to which it is applied. When f xð Þ ; y is a constant, the inference system is called a zero-order Sugeno model, which is a special case of the Mamdani system, in which the consequent of each rule is specified as a singleton fuzzy [50]. Each rule, in Sugeno model has an output given by a function. Due to this, the result is obtained through a weighted average, thus avoiding the time spent with the defuzzification process necessary in the Mamdani model. Figure 6 illustrates the concept of the TSK model.

#### 2.3 Remote sensing

2.2.2 Mamdani inference method

for rth rules are given by Eq. (3):

if x<sup>1</sup> is Ak

2.2.3 Takagi-Sugeno-Kang inference method (TSK)

and one output z, is in the form of Eq. (4).

Interpretation of the Mamdani method. Source: Adapted from Ross [46].

Figure 5.

34

<sup>1</sup> and x<sup>2</sup> is Ak

the symbol B2 refers to the consequent fuzzy of the second rule.

This equation has a very simple graphical interpretation, exemplified in Figure 5, and illustrates graphical analysis of two rules, where symbols A11 and A12 refer to the first and second fuzzy antecedents of the first rule, respectively, and symbol B1 refers to the consequent fuzzy of the first rule. The symbols A21 and A22 refer to the first and second fuzzy antecedents, respectively, of the second rule, and

Although originally proposed by Takagi and Sugeno [48], this method is also known in the literature as Takagi-Sugeno-Kang (TSK) model. This is due to the subsequent works by Sugeno and Kang [49] related to methodologies developed to identify this type of model. The fuzzy TSK model consists of an inference system capable of describing, in an exact or approximate way, non-linear dynamic systems through a set of linear, locally valid dynamic systems, smoothly interpolated, nonlinear and convex. A typical rule in a Sugeno model, which has two inputs, x and y,

Developed by Mamdani [47], the inference method is the most common in practice and literature. To begin the general view of this idea, it is considered a simple system of two rules, where each rule comprises two antecedents and one consequent. The graphic procedures herein illustrated can be easily extended and maintained for fuzzy rule bases or fuzzy systems with any number of antecedents and consequents. Two different cases of two-input Mamdani systems are considered, where the inputs to the system are scalar values and a max-min inference method is used. Thus, the Mamdani inference method for a set of conjunctive rules

Irrigation - Water Productivity and Operation, Sustainability and Climate Change

<sup>2</sup> then yk is Bk fork <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, r (3)

Remote sensing technologies are being used more and more often in the precision agricultural applications. This is because that the variables (crop stress, soil type, disease,) to be measured and controlled are very disperse in remote areas with limited wireless communications or no power supply. Also, the measurements of each variable at spatial and temporal scale are expensive and time-consuming for installing and maintaining sensors over each field. Sensors can be multispectral cameras on Satellites or mounted on Unmanned Aerial Vehicle (UAV, or "drones"). In this chapter, we focalized on the using of satellites images for agricultural applications.

Remote sensing imagery can be used for mapping soil properties, classification of crop species (land use), detection of crop water stress, monitoring of irrigation, and predicting of crop yield. The use of remote sensing in precision agriculture depends principally on the spatial, temporal, radiometric and spectral resolution. Satellite remote sensing has shown a very strong potential for irrigation management at large scale through using a different data (optical, thermal and radar) acquired from different satellites.

Optical reflectances in red and near infrared (0.4–12.5 μm) have the potential to access the vegetation indices (VI) that are directly related the different crop parameters like crop coefficient (Kc) used in estimating the crop water requirements. Several studies (e.g., [51–59]) have been specifically dedicated for

Figure 6. Graphic interpretation of the Sugeno method. Source: Adapted from [50].

estimating Kc from Normalized Difference Vegetation Index NDVI [60] and Soil Adjusted Vegetation Index SAVI [61].

However, it is important to emphasize that the commercial systems most used by farmers are not yet capable of elaborating this type of control map in the same way

Integrating Remote Sensing Data into Fuzzy Control System for Variable Rate Irrigation Estimates

Over the last decade, new information technologies, such as the geographic positioning system (GPS) and the geographic information system (GIS) have been introduced, which enabled to reduce the scale of management to the field level [81]. There are different software programs available in the market that can create maps from data point files, such as Surfer (GoldenSoftware, Inc.), ArcView (ESRI) and

The free QGIS<sup>1</sup> software will be used in this work for pre-processing and editing

As mentioned above, vegetation indices generated from remote sensing data are an important tool for the monitoring of natural or anthropogenic changes in land use and land cover. These rates have been used to estimate several vegetation parameters such as leaf area index (LAI) and amount of green biomass, as well as in the evalua-

In this study, satellite image information was used, and in this case, the reading values of NDVI—Normalized Difference Vegetation Index—is defined as the difference between Near infra-red and red reflecatnces divided by its sum. It measures the vegetative cover and its color on the land surface over wide areas. Dense and green vegetation absorbs strongly the red wavelengths of sunlight and reflect in the near-infrared wavelengths resulting high values of NDVI, near to 1. For bare soil (no vegetation), NDVI values are between 0 and 0.14 depending on the moisture and roughness of soil. The practice of plant irrigation management has inherent complexity in visualizing the symptoms of water deficit, which are difficult to detect. On some occasions, they are discovered very late, that is, when observed, their effects have already compromised the production or quality of the product. Usually these symptoms are related to leaves coloring, leaf winding, leaf angle, etc. However, it is possible to establish a correlation between the values of NDVI and the crop coefficient (Kc), [83, 84]. The estimated Kc values (Kc-NDVI) and the Kc values observed in Allen [85] for maize and soybean crops to guide the irrigation schedule during the season. Another way of relating the development of the plantation by means of remote sensing is the use of canopy temperature and infrared thermometry. A plant under water stress reduces transpiration and typically presents a higher temperature than the non-stressed crop [86], which can be a

the file provided by the i-ekbase web-tool. QGIS is an open source geographic information system (GIS), licensed under GNU General Public License. It is an official open source geospatial foundation (OSGeo) project that runs on Linux, Unix, Mac OSX, Windows and Android, and supports several formats of vectors, rasters, databases and functionalities. QGIS has a plug-in infrastructure, and it is

possible to add new features by writing plug-ins in C++ or Python.

tion of land use and management and the recovery of degraded areas [82].

powerful tool for monitoring and quantifying water stress.

Canopy temperature increases when solar radiation is absorbed [87] but, is cooled when latent energy or sweating is used to evaporate water instead of heating plant surfaces. Algorithms based on canopy temperature are strongly correlated

proposed by this work.

3.1 Geographic information system

DOI: http://dx.doi.org/10.5772/intechopen.87023

Global Mapper (Global Mapper).

3.1.1 Vegetation indices

<sup>1</sup> http://www.qgis.org/en/site/

37

For thermal data, land surface temperature (LST) derived from thermal infrared remote sensing data have been used in a variety of applications such as, among others, climate studies [62, 63], the monitoring of crop water consumption and water stress detection [64–67], vegetation monitoring [68, 69], soil moisture estimation [70–72]. Canopy temperature has long been recognized as a good indicator for crop water status and as a potential tool for irrigation scheduling. Stomatal closure is one of the first responses to plant water stress that causes a decrease in plant transpiration and thus an increase in plant temperature. An increase in plant temperature is a sign that the vegetation is undergoing water stress. The crop water stress index (CWSI) is the most frequently used index to quantify the crop water stress based on canopy surface temperature [73].

Regarding the radar images, a significant effort has been recently dedicated to exploit these images to estimate soil moisture (SM) due to (i) the high-spatial resolution achievable by synthetic aperture radars (SAR) and (ii) the advent of SAR data available at high-temporal resolution. Especially, the Sentinel-1 (S1) constellation (composed of two satellites S1-A and S1-B) potentially provides SAR data at 20 m resolution every 3 days [74]. Thus, numerous studies have investigated and exploited the sensitivity of the radar signal to SM [70, 75–80].
