Identificación de los elementos de gastos de los servicios en la gerencia

Lofti Zadeh (1965) is attributed as being the key contributor to the modern era ofFL and its applications. This study was introduced to demonstrate the vagueness of linguistics and to describe the expression of human ‘knowledge’ in a natural way (Haslum, et al, 2007). Most of the applications that involved FL were based on its reasoning process and expression in terms of understandable to both operators and experts (Perrot, et al, 2006).

33 2.2.1 Architecture of Fuzzy Logic

The basic architecture of FL is based on the concept of a ‘crisp’ input and ‘crisp’ output. Crisp means the actual data or parameter being used, is described either in quantitative or qualitative parameters. Between the crisp inputs and crisp output, all of the process is based on ‘fuzzy’ parameters which are converted at the beginning of the process. The full architecture of FL is shown in Figure 2.1.

Database (Membership

Function)

Rule Base

(If ... Then rules)

Fuzzification Interface

Decision Making Unit (Inference Operation)

Defuzzification Interface

Crisp Input _{Crisp Output}

Knowledge Base Black Box Fuzzy Fuzzy Inputs _Output Figure 2.1: Architecture of FL 2.2.1.1 Fuzzification Interface

The first step in the process is known as the ‘fuzzification processes’. It involves rule evaluation and aggregation, which is done mostly in the Knowledge Base block. There are two popular techniques which are used in this process; the Mamdani method and the Sugeno method. The advantage of the Mamdani method is in capturing expert knowledge in its entirety, whereas the Sugeno method only uses the singleton rule output, which only works well with linear techniques (Negnevitsky, 2005, J.-S.R. Jang, 1997).

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A very important part of this process is the way in which the fuzzy sets are determined. Fuzzy sets consist of an element which can be belong partly to two different sets, each of which have different memberships (Negnevitsky, 2005). In classical sets, each set has a definite answer. In deciding this, the set will be based on the inputs and outputs of the system being modelled; for example the study by (Huey- Ming, 1996), used 11 grades of risk and 11 grades of importance, from definitely unimportant to definitely important, as its fuzzy sets function.

In the design and implementation of a FL system, there is the option of using the three most popular membership functions (MFs) which are known as the triangular, Gaussian and trapezoidal functions (Negnevitsky, 2005). Each of these MFs has its own characteristics in describing the fuzzy sets, and will have a different performance rate and accuracy. For example, using triangular and trapezoidal functions means that the performance rate will be very fast, however the level of accuracy will be lower than would be the case with either of the other membership functions; this is known as the ‘normal speed versus complexity scenario’ (Xie et al., 1998). This process and implementation is performed in the Database block.

The next step is to determine the rules relationship for each of the inputs and the output, which is done in Rule Base block. This is where the inference system is used, specifically based on ‘If...then...rules’ or Bayesian rules (Negnevitsky, 2005) as below:-

IF x is Ai and IF y is Bi then z is Ci

The above rule shows typical conditions of the input function of x and y with z as the output function, the fuzzy states of Ai, Bi and Ci of i-th as the Rule Base condition.

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The design of these rules usually depends on the inputs and each of the membership functions, for example;

“Assume given a 3 inputs and a 3 membership functions for each input where the numbers of rules that can be generated based on these condition are 33 = 27 rules.”

As also described in (Negnevitsky, 2005, J.-S.R. Jang, 1997), rule evaluation in the fuzzy inference system model is based on either an ‘AND’ function or an ‘OR’ function, in terms of the fuzzy operation as algebraic product or algebraic sum, which is used to compare the inputs. The level of the truth value of the antecedent is then determined, and the consequent membership function is either clipped (correlation minimum) or scaled (correlation product) (Negnevitsky, 2005). This fuzzy operator will compare each of the inputs, and this operation takes place between the Fuzzification Interface and Knowledge Base, and will be processed in the Decision Making Unit as shown in Figure 2.1.

2.2.1.2 Defuzzification Interface

The final process is to convert all of the fuzzy values to the crisp values. This is done by defuzzification or aggregation of the rule output. Therefore, the fuzzy values that have been declared will be used to evaluate the rules, but, the final output should be a crisp value as described in (A.S. Sodiya, 2007). In order to perform the defuzzification, a number of different approaches can be used, such as; the centre of gravity or centroid, the maximum membership principle, the weighted average method, the mean-max membership method, the centre of sum method, the centre of largest area method, or the first (or last) maxima method (J.-S.R. Jang, 1997,

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Negnevitsky, 2005, Ross, 2007). The most widely used defuzzification technique is the centroid method as shown in equation (2.1), which is also discussed in later a chapter when considering clustering methods using FL.

(2.1)

2.2.3 Purpose of Using the FL

In analyzing a certain dataset, some features of the data need to be known before the output can be predicted. In one of the studies in this thesis, some data do not have any targets, which mean an unsupervised learning method needs to be used, and FL is one such unsupervised learning method in IS. In addition, FL offers advantages in converting any vagueness in linguistics, and it has a capability to explain terms based on human understanding of knowledge. FL also can be used to represent any qualitative parameter or quantitative parameter, which can help to model a food security risk level assessment. In modelling this, a lot of assumptions are made based on experience of the relationship between each of the input parameter and previous work related to this study, which will be explain in Chapter 7.