Overview / Usage

Fuzzy logic, one of the sub-branches of artificial intelligence, is a mathematical method based on the fuzzy set theory proposed by Zadeh. Logical expressions and the relationships between these logical expressions are used as the building blocks of inference systems using fuzzy logic. Fuzzy logic, which is based on fuzzy set theory, finds application in the models created by using linguistic variables without the need for a mathematical model of the system. In this study, modeling and simulation with fuzzy logic was carried out to help determine automobile prices. Matlab R2022a software was used for model creation and testing. As a result of the experiments, an MSE value of 17.5% (minimum mean square error) was achieved for the best model.

Methodology / Approach

With the development of today's social structure, different perspectives have emerged for the problems and events encountered in real life. Problems are solved using numerical and verbal data and different methods are used for this. Mathematical models can be of great benefit to people at this point. Mathematical models can help solve problems by analyzing numerical data in cases involving certainty. On the other hand, mathematical methods may be insufficient in cases involving uncertainty. In recent years, fuzzy logic, which is frequently used in solving problems with linguistic expressions instead of numerical values, is one of the artificial intelligence methods. Fuzzy logic, which has a more flexible structure than classical sets, allows us to establish a link between verbal and numerical data. Today, with the increase in consumption needs, automobile shopping has become a huge market. Especially in the sale of second-hand vehicles, there may be some problems for consumers to consciously procure the vehicle they want at the right prices. Different parameters play a role in determining vehicle prices. Vehicle age, mileage information and engine power are of great importance in the formation of prices. With the fuzzy set model proposed by Lutfi Aliasker Zade in a paper published in 1961, it was possible to make inferences with approximate values instead of exact values. Today, with the developments in information technologies, it is possible to make inferences for data evaluated with linguistic expressions such as "less", "more", "medium". In this study, a fuzzy logic model is proposed to predict vehicle prices. Forecasting used car prices with a fuzzy model has not found much place in the literature. In their study, Syahputra et al. created a model for predicting vehicle prices using the sugeno method and achieved an accuracy of 96.36% (Syahputra et al.).

Fuzzy Logic

In classical logic, classifications are definite, i.e. an element is either an element of a set or it is not, there can be no partial membership. Classical sets have the logic of 0 and 1.[3] In classical sets, something either "exists" or "does not exist". Where fuzzy logic differs from classical logic is that it allows the computer to see intermediate values. It is the process of modeling information with the help of blurring and rinsing processes within various rule bases. A fuzzy system consists of a fuzzy set, linguistic expressions, membership functions, if-then rules, fuzzification, rinsing, inference parts and finally the person's experience and experience. Inputs and outputs are crisp values. It is a set logic model proposed by Lutfi Aliasker Zade in a paper published in 1961. Lütfi Rahim Oğlu Askerzade, better known by his full name Lütfi Zadeh, stated the principles of fuzzy logic as follows;

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In fuzzy logic, approximate values are used instead of precise values.

For fuzzy logic, information is defined by linguistic expressions such as very little, little, small, large.

In fuzzy logic, all values are represented by a membership degree in the range [0-1].

Every logical expression can be transformed into a fuzzy statement.

Fuzzy logic is a suitable method for systems whose mathematical model is very complex and difficult.

A fuzzy process (fuzzy process) usually consists of three separate processes. These units are the fuzzifier unit, the rule processing unit, the clarifier unit and the output information, respectively. Figure 1 shows a general fuzzy system structure (Kıyak et al., 2003) (1). In the fuzzy system structure, the fuzzifier unit is the first unit of the fuzzy system. For the data coming to this unit, each of them is assigned a membership value and converted into a linguistic structure. The linguistically transformed data is transferred to the rule processing unit. The data transferred for rule processing is combined with rule processing information in this unit. Rule bases are structures in which one or more fuzzy propositions are connected with logical connectives to show the relationship between fuzzy sets. In rule bases, the conjunction "and" denotes intersection and the conjunction "or" denotes union. In the last step, the results obtained by using logical decision propositions appropriate to the structure of the problem are sent to the clarifier unit. In the fuzzy set relations sent to the clarifying unit, another scale change is made and each of the fuzzy information is converted into real numbers (Kıyak et al., 2003) (1). Blurring

It is necessary to fuzzify the intervals of change that appear as classical sets and to create fuzzy sets of all variables belonging to the system (Coşkun, 2019) (8). In order to create fuzzy sets, it should be ensured that the items that can be found in a certain range have values between 0 and 1. Items with values between 0 and 1 are considered to contain uncertainty, and when we talk about non-numerical situations of uncertainties, we talk about fuzziness (2) (Şen, 2020).

The membership functions considered in the fuzzification process should be suitable for the structure of the problem and the intended model. In general, membership functions are based on intuitive, mathematical, geometric or statistical approaches

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The main methods used to determine membership functions;

a) Intuition,

b) Inference,

c) Grading,

d) Angular fuzzy sets,

e) Artificial neural networks,

f) Genetic algorithms,

g) Inferential reasoning (Kıyak et al., 2003) (1).

The usefulness of fuzzy sets is based on the ability to create membership degree functions suitable for different concepts. For convenience, the most preferred functions in the literature are "triangle" and "trapezoid" (Kıyak et al., 2003; Yen , 1999)(1)(3).

The representation of the elements of any fuzzy set with triangular membership function, trapezoid membership function and bell curve (Gaussian) membership function are given in Figure 2, Figure 3 and Figure 4. The mathematical expression of the specified membership function is shown with the expressions under the graphs (Kıyak et al., 2003; Nguyen et al., 2018) (1)(4). 

Rule Processing Unit

In fuzzy logic, rules enable the formulation of conditional situations in the form of 'if ..., then ...' (Piegat, 2013) (5).	In the designed system, input variables are converted into verbal values and the fuzzy inference step is applied based on rules and the values of verbal variables are calculated in the output function (Al, 1998) (6). The fuzzy rule should be designed as "if ..., then ..." statements with verbal input and output terms (Negoita et al., 1987) (7). Fuzzy inference calculations have two components. There is a clustering component with the "if" statements and an ordering component with the "whether" parts. For example, in the statement 'If X is A, then let Y be B', the values symbolized by A and B are verbal words. It shows to which situations the values X and Y belong. In engineering projects and designs, precise numerical results are needed in order to make calculations and inferences correctly. Accordingly, in artificial intelligence studies, fuzzy outputs should be converted into precise numerical values. All of the operations performed to transform fuzzy information into precise results are called as "stabilization operations" (Kıyak et al., 2003) (1).

The fuzzy set result obtained as a result of the merging is subjected to the process of clarification and the numerical result is obtained. As can be seen in the literature, the most frequently used methods in the literature are "Centroid Method", "Area Centroid Method", "Mean of Maxima (MOM) Method", "Smallest of Maxima (SOM) Method", "Largest of Maxima (LOM) Method", "Weighted Average Method", "Center of Sums Method", "Center of Largest Area Method" (Coşkun, 2019)(8).

Method

The first step for applying fuzzy logic to a system is to determine the input and output parameters of the system. Considering the price parameters of second-hand vehicles, mileage, age and horsepower value are the most important factors. It is determined as the only output value in the system. The output value for mileage, age and horsepower value is the price. According to the effects of input and output parameters on the problem to be modeled, membership function numbers, names, lower and upper limits of all parameters were determined. After determining the membership functions, lower and upper limits of the parameters required to build the model, 14 rules were created to establish the necessary relationships between the parameters affecting the system. The model was designed on Matlab R2022a software. A few of these rules are given below as examples.

o If age is low and mileage is low and horsepower (HP) is high, the price is high.

o If age is high and mileage is high and HP is low, price is low.

o If age is medium and mileage is high, price is low.

o If age is medium and mileage is medium, price is medium.

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The membership functions are shown in Figure 5, Figure 6 and Figure 7 for the input parameters vehicle age, mileage and HP (vehicle engine horsepower) respectively. Price information was set as the output parameter. There are 10 fields in the data set used to compare the results. However, 3 fields were determined as attributes for the model created. Comparisons and tests were made in line with the determined fields.

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Technologies Used

Fuzzy Logic, Matlab and FIS

Documents and Presentations