1. The Least Squares Ratio (LSR) Approach to
Fuzzy Linear Regression Analysis
International Conference for Engineering and Technology, May 2016, Toronto
e-mail: muraty@jforce.com.tr
MURAT YAZICI, M.Sc.
Sr. Data Scientist & Researcher

2. Murat YAZICI, M.Sc.
Contents
 Introduction: The Regression Model and Its Usage Areas
 What is the problems while setting up a regression model?
 The Least Square Ratio (LSR) Method and Its Benefits
 The Fuzzy Linear Regression Model defined D’Urso & Gastaldi
 A LSR Approach to Fuzzy Linear Regression Analysis
 A Case Study of The LSR vs. The OLS Approach
- The Case Study :The effects of the position of a video display terminal on an operator
. With one independent variable
. With several independent variables
 Conclusion and Future Work
 Who is JForce IT Company?
 References
 Thanks…
International Conference for Engineering and Technology, May 2016, Toronto

3. Murat YAZICI, M.Sc.
Introduction: The Regression Model
International Conference for Engineering and Technology, May 2016, Toronto

4. Murat YAZICI, M.Sc.
Introduction: Its Usage Areas
International Conference for Engineering and Technology, May 2016, Toronto
Some of usage areas of The Regression Analysis;
 Economy
 Finance
 Business
 Law
 Meteorology
 Medicine
 Biology
 Chemistry
 Engineering
 Education
 Sports
 History
 Sociology
 Psychology

5. Murat YAZICI, M.Sc.
What is the problems while setting up a regression model?
International Conference for Engineering and Technology, May 2016, Toronto
While setting up a linear regression model, Ordinary Least Square (OLS) Method is generally used.
The OLS Method: One of the biggest problems of the OLS
method is that it could not successfully
estimate coefficients in case of outliers
and/or extrem values.

6. Murat YAZICI, M.Sc.
The Least Square Ratio (LSR) Method and Its Benefits
The OLS method aims to estimate observed values with zero error: we can indicate this goal by ,
or . Hence, the ordinary least squares approach satisfies this aim by finding the regression
parameters minimizing the sum of . From the error definition , it is clear that, the size
of error does not depend on the size of . For example, consider estimating 100 as 200 and 1,000 as
1,100: we get the same error −100. However, another point of view says that for the first estimation
there is 100% error, but only 10% for second.*
The Least Square Ratio (LSR) starts with the same goal as in OLS. However, it proceeds by dividing
through by and so is obtained under an assumption of . Hence, it is obvious that,
equations and are raised by basic mathematical operations. This final
equation is taken into account as the origin of the LSR which minimizes the sum of .*
International Conference for Engineering and Technology, May 2016, Toronto
* O. Akbilgic, E.D. Akinci, A Novel Regression Approach: Least Squares Ratio, Communications in Statistics - Theory and Methods 38:9 (2009) 1539-1545.

7. Murat YAZICI, M.Sc.
The Least Square Ratio (LSR) Method and Its Benefits
International Conference for Engineering and Technology, May 2016, Toronto
The LSR Method: One of the biggest problems of the OLS
method is that it could not successfully
estimate coefficients in case of outliers
and/or extrem values.

8. Murat YAZICI, M.Sc.
The Fuzzy Linear Regression Model defined D’Urso & Gastaldi
A double linear adaptive fuzzy regression model
defined D’Urso and Gastaldi is as follows:
International Conference for Engineering and Technology, May 2016, Toronto
where
where

9. Murat YAZICI, M.Sc.
A LSR Approach to Fuzzy Linear Regression Analysis
International Conference for Engineering and Technology, May 2016, Toronto
The proposed LSR approach to the double linear adaptive fuzzy regression model aims to minimize the
euclidean distance between the observed ratio values and the obtained ratio values .

10. Murat YAZICI, M.Sc.
A Case Study :The effects of the position of a video display terminal on an operator
International Conference for Engineering and Technology, May 2016, Toronto

11. Murat YAZICI, M.Sc.
A Case Study :The effects of the position of a video display terminal on an operator
International Conference for Engineering and Technology, May 2016, Toronto

12. Murat YAZICI, M.Sc.
A Case Study :The effects of the position of a video display terminal on an operator
International Conference for Engineering and Technology, May 2016, Toronto

13. Murat YAZICI, M.Sc.
A Case Study :The effects of the position of a video display terminal on an operator
International Conference for Engineering and Technology, May 2016, Toronto

14. Murat YAZICI, M.Sc.
Conclusion and Future Work
International Conference for Engineering and Technology, May 2016, Toronto
In this study, a regression method called Least Squares Ratio (LSR) approach to fuzzy linear regression
was explained as an alternative method to other techniques. According to Mean Absolute Error
(MAE), we can say that the LSR Approach gave better results than the OLS Approach. In addition to
this, in the case of the presence of outliers and/or extreme values, the LSR Approach will show better
performance than OLS because the LSR Approach is more sensitive to them. For future work, the LSR
and OLS Approaches can be compared to which technique give better results by using different error
criteria. Also, their performance can be explored in the case of different fuzzy numbers such as non-
symmetric triangular and trapezoidal fuzzy numbers etc.

15. Murat YAZICI, M.Sc.
About JForce IT Company
 JFORCE is founded in 2003 with a Focus in Insurance, Banking and IBM solutions.
 Acting as a software house and system integrator JForce is delivering innovative
solutions with state of the art technologies.
 With a team of 40 and over 85 Certifications JForce is one of the biggest solution
providers of IBM in Turkey.
 Key Technology focus is in Systems&Middleware : Application Servers, Integration,
Business Process Management, Business Rules Management, Complex Events ,
Statistical Modelling
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16. Murat YAZICI, M.Sc.
JFORCE Key Solution Areas for Insurance
JForce is serving Insurance Market with
• Core Insurance Solutions (NTT Data Partnership)
• Claims Process Automation & Analytic Dashboards
• Fraud & Leakage Management
• Underwriting Automation / Contract Management
• Dynamic Pricing
• Telematics and Related Mobile Applications
• Predictive Customer Intellegence, Realtime Marketing and Event Management
• Service Integration
• Provision Automation and
• Online Pharmacy Automation Solutions.
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17. Murat YAZICI, M.Sc.
Our Global Partnerships
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18. Murat YAZICI, M.Sc.
Awards & Recognitions
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2003 IBM Best Project of The Year
2004 IBM Best System i Partner
2004 INDEX Best Performing Partner
2005 IBM Best System i Partner
2006 IBM Best System i Partner
2006 ORACLE Partner Network
2007 IBM Best System i Partner
2008 IBM TÜRK 70. YIL ÖZEL ÖDÜLÜ
2009 IBM Best Performance Websphere
2009 Best Performance – Power i
2009 VISION SOLUTIONS Quota Achievement
2012 IBM Best Project of The Year
2013 Best Performing DB2 Partner
2014 IBM Most Competitive Project of The Year
2015 IBM Technical Accelence Award in 3 Categories

19. Murat YAZICI, M.Sc.
Some of Our References
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20. Murat YAZICI, M.Sc.
Contact Us
International Conference for Engineering and Technology, May 2016, Toronto
www.jforce.com.tr
Göztepe Mh. Göksuevleri Sit. Sardunya Sk.
B212B 34810 Anadoluhisari / Istanbul, Turkey
Phone: 0090 216 668 0290
Fax: +90 216 668 02 95
E-mail: info@jforce.com.tr

21. Murat YAZICI, M.Sc.
References
International Conference for Engineering and Technology, May 2016, Toronto
1. B. Heshmaty, A. Kandel, Fuzzy linear regression and its applications to forecasting in uncertain environment, Fuzzy Sets Systems 15:2 (1985)
159-191.
2. C. Cheng, E.S. Lee, Fuzzy Regression with Radial Basis Function Network, Fuzzy Sets and Systems 119:2 (2001) 291-301.
3. C. Kao, C.L. Chyu, Least-Squares Estimates in Fuzzy Regression Analysis, European Journal of Operational Research 148 (2003) 426-43.
4. D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
5. H. Tanaka, Fuzzy data analysis by possibilistic linear models, Fuzzy Sets Systems 24 (1987) 363-375.
6. H. Tanaka, S. Uejima, K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybernet 12:6 (1982) 903-907.
7. H. Tanaka, J. Watada, Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets Systems 27 (1988) 145-160.
8. H. Tanaka, H. Ishibuchi, Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters, Fuzzy Sets
Systems 41 (1991) 145-160.
9. H. Tanaka, H. Ishibuchi, S. Yoshikawa, Exponential possibility regression analysis, Fuzzy Sets Systems 69 (1995) 305-318.
10.H.J. Zimmermann, Fuzzy Set Theory-and Its Application, Kluwer Academic Press, Dordrecht, 1991.
11.J.J. Buckley, Fuzzy Probability and Statistics, Springer, 2006.
12.O. Akbilgic, E.D. Akinci, A Novel Regression Approach: Least Squares Ratio, Communications in Statistics - Theory and Methods 38:9 (2009)
1539-1545.
13.P. D’Urso, T. Gastaldi, A Least-Squares Approach to Fuzzy Linear Regression Analysis, Computational Statistics & Data Analysis 34 (2000)
427-440.
14.P.T. Chang, E.S. Lee, S.A. Konz, Applying fuzzy linear regression to VDT legibility, Fuzzy Sets Systems 80:2 (1996) 197-204.
15.W. Xizhao, H. Minghu, Fuzzy linear regression analysis, Fuzzy Sets Systems 51 (1992) 179-188.

22. Thank you!..
MURAT YAZICI, M.Sc.
Sr. Data Scientist & Researcher
LinkedIn: https://tr.linkedin.com/in/muraty1
E-mail: muraty@jforce.com.tr
Phone: 0090 539 601 6854