FOOD SECURITY RISK LEVEL ASSESSMENT: A FUZZY LOGIC-BASED APPROACH

A fuzzy logic (FL)-based food security risk level assessment system is designed and is presented in this article. Three inputs—yield, production, and economic growth—are used to predict the level of risk associated with food supply. A number of previous studies have related food supply with risk assessment for particular types of food, but none of the work was specifically concerned with how the wider food chain might be affected. The system we describe here uses the Mamdani method. The resulting system can assess risk level against three grades: severe, acceptable, and good. The method is tested with UK (United Kingdom) cereal data for the period from 1988 to 2008. The approach is discussed on the basis that it could be used as a starting point in developing tools that may either assess current food security risk or predict periods or regions of impending pressure on food supply.


INTRODUCTION
In the context of this work, risk will be defined as the probability of a negative function that attempts to describe the possible adverse pressure on the system caused by a hazard (Meltzer et al. 2003;Wang, Li, and Shi 2008). Risk assessment has become increasingly important from a research perspective in terms of either an area of application or society itself, and it is considered a valuable tool in most studies in which food security projections are linked to decision support systems. Most of such work will indicate risk levels that are either minor or major but otherwise are mainly qualitative. Advanced risk assessment protocols are used in many areas as aids to decision making. For example, in the construction industry, where the practice is comparatively mature, the techniques of fault tree analysis, event tree analysis, Monte Carlo analysis, scenario planning, and sensitivity analysis are prevalent (Peihong and Jiaqiong 2009).
Although there are many accepted risk assessment methods, many scientists and engineers are trying to improve the techniques in order to produce more accurate results. For example, the analysis hierarchy process (AHP) decision-making technique in the construction industry is improving risk assessment, but it has a drawback in that it can deal only with definite scales and measured commodities; it cannot solve involved uncertainties and subjectivities (Peihong and Jiaqiong 2009). Fuzzy logic (FL) technique is an alternative technique that is becoming more frequently used to improve the performance of risk assessment systems (Zeng, An, and Smith 2007). FL can work effectively with many parameters and nonuniform variables, which suggests that it can deal with most of the drawbacks in previous and more conventional techniques. The application of FL to predict challenges to food security are evaluated in this study.

Food Security
Food security is a broad area. On the macro scale, it has largely been relegated to international agencies. On the micro scale it has been devolved to national government agencies. However, in the last few years, rising commodity prices, combined with agricultural reactions or consequences of climate change, have contributed to its moving to center stage in policy analysis and interventions (Initiative 2009). The definition of food security is much debated; for the purposes of our research, it was taken in the usually understood sense of ''food security exists when all people, at all times, have physical and economic access to sufficient, safe and nutritious food that meets their dietary needs and food preferences for an active and healthy life'' (FAO 2006). Some influential authors (Peihong and Jiaqiong 2009) indicate that the main factors in food security at a national level are: food availability, according to the needs of the person (encompassing food prices, distance to shops, available income to spend on food); food affordability, nutritional contents, safety, food-system resilience and consumer confidence (DEFRA 2009(DEFRA , 2010. Each of these factors can be represented by various indicators such as trends in global output of food (from farm to end products), land-use changes, diversity of supply, energy dependency of food chain, income factors, and trends in food-borne pathogen cases where monitoring could be difficult because of long-term effects from pathogenic bacteria such as salmonella, listeria, E. coli O157, and campylobacter (DEFRA 2010). Each of the indicators is related to the food chain processes (Ding, Li, and Feng 2007) and each is evaluated or recorded from imprecise inputs. Most of the factors are not fully controllable, in that it is not about just the resilience or success of the food chain-it is also about consumer demand and the supply channel such as retail outlets and restaurants; therefore, it is difficult to use a conventional data-based approach, which would require precise information to describe every single interaction.
In contrast, FL systems offer a number of advantages compared with conventional data-based approaches. Some of the main advantages are that they can be easily implemented and tuned, and they use ''If-Then'' rules that will generate output based on imprecise inputs. However, to make them more effective, FL systems require a great deal of data parameters or expert information. There are a few previous examples of FL being applied to specific elements of the food chain and related food security; for example, China's grain security warning study (Jianling and Yong 2010a;2010b;Yong and Jianling 2010), crop control (Ahmed, Damiani, and Tettamanzi 1999) and the gari fermentation plant (Odetunji and Kehinde 2005).
In this article, we are concerned with examining the risk of national food insecurity by using an FL technique. The system was designed such that it is able to determine the overall level of prevailing food security risk by monitoring various but independent risk elements within food supply systems. The rest of this article is organized as follows: the next section presents the Methodology, the section following that contains Results and Discussions, and the final section presents the conclusions.

METHODOLOGY
Lotfi Zadeh is attributed with being the key contributor to the modern era of FL and its applications. The methodology was introduced to cope with vagueness in linguistics and the challenges of expressing human knowledge in a natural but generally imprecise way (Haslum, Abraham, and Knapskog 2007). Most of the applications that involved FL were based on its reasoning process and its ability to express outputs in understandable terms (Perrot et al. 2006). Given the multiple complexities involved in evaluating risk in food security and food supply chains, an FL model was attempted by Wang, Li, and Shi (2008). This principle is applied at the input to the level of risk on food security in the UK (Figure 1).

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M. K. Abdul Kadir et al. Our model in Figure 1 uses UK crop yield (defined as the monthly farm gate crop output), UK crop production (defined as crops that are processed into food products), and UK economic growth (defined as percentage of gross domestic product, GDP) as the inputs to determine the risk level, which is the system output. The work by Monty P. Jones (Jones) concerning a study in sub-Saharan Africa, showed that the first two inputs are good indicators of overall food availability. The study also indicated that economic growth was strongly associated with food security. Our objective is to use the FL technique to turn these semi-precise or qualitative measures into quantitative assessment outcomes. Each of the input and output processes is performed in an FL black box. In this scenario, the process that is conducted inside the black box is a fuzzy inference process.
The first step in the fuzzy inference process is called a fuzzification process. It involves rule evaluation and aggregation using the Mamdani method. This method was selected because it is widely accepted and is suited to capturing expert knowledge. If it is compared to the Mamdani method, the Sugeno method uses the singleton rule output, which works well only with linear techniques (Jang and Gulley 1997;Negnevitsky 2005). A very important part of this process is how the fuzzy sets are delimited. Rules need to be set based on grades of importance of inputs and outputs of the system being modeled (Huey-Ming 1996).
In our model, each of the inputs has been chosen to have three fuzzy sets that will determine the degree of each of the inputs as shown in Table 1. The ranges refer to the normalization of the corresponding crisp input value based on its universe of discourse. For this study, cereal data is For cereal crop yield, the input value will be derived from high yield, medium yield, and low yield as its fuzzy set, which was determined based on the highest and lowest value and divided into three lots. This approach also applies in the case of crop production and economic growth as shown in Figure 1. In the case of the output, the fuzzy set function is shown in Table 2, which indicates the fuzzy sets and their ranges. The ranges of each input and output are determined by referring to the data value in the UK as described in ''Testing the System with the Data for the Input,'' where the maximum and minimum value of each input parameter for the period of years is specified.
In the design and implementation of an FL system (Negnevitsky 2005), the option exists to choose which of the three most popular membership functions to use: triangular, Gaussian, or trapezoidal. In this work, initially we chose to use the triangular function for the inputs and a trapezoidal function for the outputs of our model. We will explore the other options later if necessary. Using triangular and trapezoidal functions means that the performance rate of the fuzzification process will be very fast, although the level of accuracy will be lower than with either of the other membership functions: this is the normal speed versus complexity scenario (Xie, Xiong, and Church 1998).
The next step is to determine the rule relationship for each of the inputs and the output. This is where the Bayesian rules (Negnevitsky 2005) and ''ifthen'' rules were used. Given three inputs and three membership functions, the numbers of rules that can be generated is 3 3 ¼ 27 rules (Table 3).
Here is an example of the fuzzy rule, which relates the input and the output by using the ''if-then'' technique: ''If cereal yield is high and cereal production is high and economic growth is high, then the risk level will be good.'' A similar rule statement will apply for the remaining 26 rules in Table 3. Next, in the rule evaluation, an AND function is used as a fuzzy operator to compare each of the inputs. This function also known as the algebraic product function (Negnevitsky 2005).
For our example, to get the crop value (crisp value), the fuzzy output value needs to be defuzzifed or to be aggregated at the rule output (Sodiya, Onashoga, and Oladunjoye 2007). In order to perform the defuzzification, a number of different approaches maybe used; see for example, Jang, Sun, and Mizutani (1997) and Negnevitsky (2005). Here, we use either the center of gravity or centroid as the defuzzification technique.

Testing the System with the Data for the Input
In order to test the system, the data is taken from an online database such as World Bank (2010) and the Food and Agriculture Organization (FAO; FAO 2010). The data that we used relate to cereal yield and cereal Food Security Risk Level Assessment: A Fuzzy Logic-Based Approach production from 1988 to 2008 because the longer the period of data, the higher the testing value that we can analyse and study for this model. The cereal yield unit is in hectogram=hectare (Hg=Ha) and the cereal production unit is in tons. The same goes for the economic growth data, which are based on growth as a percentage of GDP for the period. All the data have been normalized because the system input fuzzy set is 0 to 1. We will present the results and discuss them in the next section of this article.

RESULTS AND DISCUSSIONS
The simulation was run in the MATLAB 2010 environment, and Figure 2 shows the fuzzy model of the risk assessment system based on the Mamdani method. The system uses the 27 fuzzy rules and the centroid defuzzification to defuzzify the output.
The overall result of the system will be determined by the relationship between the three inputs and the one output as shown in Figures 3, 4, and 5. This relationship between each input and the output was to show the changing pattern of the models based on the if-then rules generated by the system in Figure 6.
The system output depends on the 27 rules (see Table 3), that have been created. In order to clearly show the effect of the membership function, the results of all of the rules are shown in Figure 6, which shows the membership function used for each input and output. Figure 7 shows the FIGURE 2 The model for our FL-based risk assessment system.

FIGURE 4
Output ¼ risk level, inputs ¼ economic growth and cereal yield.

FIGURE 3
Output ¼ risk level, inputs ¼ cereal production and its yield.

FIGURE 5
Output ¼ risk level, inputs ¼ economic growth and cereal production.
Food Security Risk Level Assessment: A Fuzzy Logic-Based Approach 57 overall membership function for each of the inputs and Figure 8 shows the membership function of the output. In order to verify the results, crisp outputs are used to test the system when real data are used as the inputs. The results show that every year the assessment of the risk level of food security changed depending on cereal yield, cereal production, and economic growth. For example, in 1988, the UK cereal yield was 53993 Hg=Ha, cereal production was  M. K. Abdul Kadir et al. food security risk level value almost rose to 0.9, which is a severe condition. Our system shows that, although a high quantity of yield and high production should lead to high food security, when economic growth is low, people will try to pay the lowest price for their food, which means that fewer resources are expended by the consumer in order to get the best food. Although some people will often be prepared to pay for a given commodity even if they cannot afford it, this will not entirely affect the system because it is assumed to be a minority case. So, an observation based on this is that food is likely to be wasted, especially the high-quality food, which is most expensive. But, if the economic growth is high and the cereal yield is low, the food security is low and there may not be enough food for everyone. This relationship is shown in Figure 9, where, based on the real data, for most years, the risk level is acceptable (0.2-0.8). Only in 1992 and 1996 is there a good (below 0.2) food security risk level.

CONCLUSIONS
The work presented here has demonstrated how an FL-based system might be used to predict food security risk levels using data that are relatively inconsistent. In this case, the study is concerned with the UK food security. However, the inputs were based on relatively poor-quality information in terms of knowledge and the fact that we were using a weighting estimation that is equal to 1. Weighting estimation can be used to weight the importance of the input, but in this study case, all inputs were given the same importance. The FL can also be developed further to determine the risk level thoroughly and specifically.