# Fuzzy Rule Based Classification Essay

^{1}Department of Biostatistics, Faculty of Health, Diabetes Research Center, Mazandaran University of Medical Sciences, Sari 4817844718, Iran^{2}Department of Radiology, Faculty of Medicine, Mazandaran University of Medical Sciences, Sari 4817844718, Iran^{3}Department of Biostatistics, Faculty of Health, Zabol University of Medical Sciences, Zabol, Iran^{4}Mazandaran Heart Center, Mazandaran University of Medical Sciences, Sari 4817844718, Iran

Copyright © 2015 Reza Ali Mohammadpour et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The aim of this study was to determine the accuracy of fuzzy rule-based classification that could noninvasively predict CAD based on myocardial perfusion scan test and clinical-epidemiological variables. This was a cross-sectional study in which the characteristics, the results of myocardial perfusion scan (MPS), and coronary artery angiography of 115 patients, 62 (53.9%) males, in Mazandaran Heart Center in the north of Iran have been collected. We used membership functions for medical variables by reviewing the related literature. To improve the classification performance, we used Ishibuchi et al. and Nozaki et al. methods by adjusting the grade of certainty of each rule. This system includes 144 rules and the antecedent part of all rules has more than one part. The coronary artery disease data used in this paper contained 115 samples. The data was classified into four classes, namely, classes 1 (normal), 2 (stenosis in one single vessel), 3 (stenosis in two vessels), and 4 (stenosis in three vessels) which had 39, 35, 17, and 24 subjects, respectively. The accuracy in the fuzzy classification based on if-then rule was 92.8 percent if classification result was considered based on rule selection by expert, while it was 91.9 when classification result was obtained according to the equation. To increase the classification rate, we deleted the extra rules to reduce the fuzzy rules after introducing the membership functions.

#### 1. Introduction

In the past years, fuzzy if-then rule-based systems were used basically to control problems, while nowadays they are mainly applied in classification tasks [1–7]. There are many methods for automatically generating and learning the fuzzy if-then rules from numerical data for pattern classification problems [2, 4, 5, 8, 9].

The concepts of linguistic statement have been introduced by Zadeh [10] and it is crucial that we see each attribute as linguistic value showed by fuzzy numbers with trapezoidal membership function [11, 12].

After generating the volunteer rule, a set of rules must be chosen to structure the rule based on the classifier. In this paper, we assume a number of prespecified fuzzy sets given by expert’s knowledge for each input attribute [13]. The performance of resulting classifiers can be enhanced by using rule weighting [14]. Therefore, our study can have effect on generating, weighting, and selecting rules based on expert opinions or systems outputs.

Therefore, the total number of fuzzy if-then rules generated by partitioning each attribute into fuzzy subsets in an -dimensional pattern classification is defined as [4, 5, 15]. In this work, we adjusted the grade of certainty of fuzzy if-then rules when there was misclassification of an input pattern in an error-correction method [15].

Coronary artery disease (CAD) is the most common cause of mortality in worldwide population and has a high prevalence of mortality rate in both developing and developed countries [16]. Many risk factors such as age, sex, high blood pressure, diabetes, obesity, smoking, family history of coronary artery disease, and cholesterol (LDL) have essential role in CAD [17]. Some risk factors such as sex and diabetes are crisp, whereas others are fuzzy sets.

The gold standard method for the diagnosis of CAD is coronary angiography (CA). Since CA is a costly and invasive procedure needing technology and high level of technical experience, it cannot be used to screen large population [18–20]. Therefore, noninvasive alternative methods for coronary angiography are necessary. A number of noninvasive CAD diagnosis methods have been proposed in literature [21], namely, exercise stress test and Single Photon Emission Computed Tomography (SPECT) or scintigraphy and Echo. However, the diagnosis accuracy of these tests is not as high as that of coronary angiography. Some studies showed that these medical tests do not have an accurate result and fuzzy set theory can enhance their accuracy [22–25]. Moreover, the diagnosis accuracy of a combination of the results of noninvasive clinical tests and other clinical-epidemiological attributes has been improved by using fuzzy models [26]. Fuzzy systems have been proposed and used to determine the cardiovascular diseases and to assess the risk factors due to the ambiguity and uncertainty of the diagnostic process [27, 28].

Fuzzy rule-based classification system is one of the fuzzy systems. In recent years, fuzzy classifier methods have been commonly used in medical diagnosis. In the literature there are a lot of studies that have worked on the classification of medical data (on cancer and cardiology) using fuzzy classifiers [29, 30]. In 2004, Vig et al. employed fuzzy set theory for the diagnosis of CAD [31]. Allahverdi et al. designed a fuzzy expert system to determine coronary heart disease risk [32] and P. Srivastava and A. Srivastava conducted similar study in India [33] and some of investigators studied improving fuzzy decision systems for CAD diagnosis.

Clinical importance or relevance of features (input variables) in cardiology diagnostic tests can introduce weights for interpretable fuzzy rule selection. CAD diagnosis is a complex and important problem. Some of rules are clinically acceptable and desirable by physicians. In this paper, we added the result of MPS to other attributes for generating fuzzy rules according to physician knowledge and supervised classification with labeled data. Data set is classified using Ishibuchi et al. [34–36] weighted fuzzy rule-based classifier to diagnose CAD and 3 levels of severity of CAD.

The aim of this study was to determine the accuracy of fuzzy rule-based classification that could noninvasively predict the CAD based on myocardial perfusion scan test and clinical-epidemiological variables.

After Introduction in Section 1 we continued, in Section 2, generating, learning, and weighting fuzzy if-then rules. Finally, in Sections 3 and 4, we showed application results and discussion.

#### 2. Methods: Weighting Fuzzy Classification System

##### 2.1. Fuzzy If-Then Rule

Let us suppose that our pattern classification problems are training patterns , with -class -dimensional problem [5, 7, 30].

First, all attribute values of the given training pattern are transformed in the unit interval . Thus, the pattern space into the -dimensional pattern classification problem uses unit hypercube [5, 6, 34]. For an -dimensional, -class problem, we apply fuzzy if-then rule of the following form:where is the label of the th fuzzy if-then rule, is the total number of fuzzy if-then rules, is the pattern vector -dimensional, presents antecedent fuzzy sets for the th attribute, represent a consequent class (i.e., one of the classes), and is a certainty grade of the fuzzy if-then [2, 5, 9, 13, 15, 34, 35].

As antecedent fuzzy sets we employ trapezoidal fuzzy sets, where we display other partitions of the unit interval into fuzzy sets [2, 36].

Using (1), we generate fuzzy if-then rule that consists of two below steps. The first one is specifying membership function of antecedent fuzzy sets and the second one is determining consequent class and certainty grade of the fuzzy rule [2, 5, 15]. The antecedent part of the fuzzy if-then rules is initialized manually [2]. For each training pattern, the concept of a weight is applied. The weight of misclassified/rejected patterns is observed as a cost of misclassification or rejection. When a training pattern is misclassified, then the adjustment of fuzzy rules arises. In this study, we can determine both consequent class and the grade of certainty for all rules of the following type.

*Step 1. *Calculate the compatibility grade of training patterns using product as T-norm:where is the membership function of fuzzy sets .

*Step 2. *For each class can be calculated according toAnd is the weight of the training pattern.

*Step 3. *Find class that has largest sum of :Note that if two or more classes take the maximum value of (4), then the consequent class of the fuzzy rule cannot be individually determined, so is also specified as . Let the grade of certainty of fuzzy rule be . If only class takes the maximum value, let be class . The grade of certainty can be assigned as follows:With is the total number of classes.

After generating fuzzy if-then rules by (1), both the consequent class and the grade of certainty can be determined for all rules; then a new pattern according to the following procedure can be classified.

*Step 1. *For class , calculate as

## Abstract

The aim of this research is to present a detailed step-by-step method for classification of very high resolution urban satellite images (VHRSI) into specific classes such as road, building, vegetation,*etc.*, using fuzzy logic. In this study, object-based image analysis is used for image classification. The main problems in high resolution image classification are the uncertainties in the position of object borders in satellite images and also multiplex resemblance of the segments to different classes. In order to solve this problem, fuzzy logic is used for image classification, since it provides the possibility of image analysis using multiple parameters without requiring inclusion of certain thresholds in the class assignment process. In this study, an inclusive semi-automatic method for image classification is offered, which presents the configuration of the related fuzzy functions as well as fuzzy rules. The produced results are compared to the results of a normal classification using the same parameters, but with crisp rules.

*The*overall accuracies and kappa coefficients of the presented method stand higher than the check projects. View Full-Text

*Keywords: *fuzzy rule based systems; object-based image classification; very high resolution satellite imagery; urban land coverfuzzy rule based systems; object-based image classification; very high resolution satellite imagery; urban land cover

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

## Scifeed alert for new publications

**Never miss any articles**matching your research

**from any publisher**

- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now

## Share & Cite This Article

**MDPI and ACS Style**

Jabari, S.; Zhang, Y. Very High Resolution Satellite Image Classification Using Fuzzy Rule-Based Systems. *Algorithms***2013**, *6*, 762-781.

**AMA Style**

Jabari S, Zhang Y. Very High Resolution Satellite Image Classification Using Fuzzy Rule-Based Systems. *Algorithms*. 2013; 6(4):762-781.

**Chicago/Turabian Style**

## 0 comments