Parallel Computing in Fuzzy Decision Making Systems

Abstract

In some decision problems, the numbers of alternatives, criteria and decision-makers are very high. Therefore the calculation process becomes more difficult, time consuming and complex. To achieve these complex tasks in a shorter time, popular technologies such as parallel computing are available to use. In this study, design and implementation of parallel computation in a fuzzy decision making system which consists of the methods: Fuzzy Analytic Hierarchy Process (FAHP) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) was investigated. Parallel computing was carried out in FAHP phase that is most intensive phase of calculation. Proposed method was tested in homogeneous and heterogeneous computers separately and results were discussed.

Keywords

• Fuzzy decision making, Parallel computing, Fuzzy analytic hierarchy process, TOPSIS.

Bulanık Karar Verme Sistemlerinde Paralel Hesaplama

Öz

Bazı karar problemlerinde, alternatif, kriter ve karar vericilerin sayısı çok yüksektir. Bu yüzden hesaplama işlemi daha zor, zaman alıcı ve karmaşık bir hal alır. Bu karmaşık işlemleri daha kısa sürede gerçekleştirilebilmek için paralel hesaplama gibi popüler teknolojiler mevcuttur. Bu çalışmada, Bulanık Analitik Hiyerarşi Süreci (BAHS) ve TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) yöntemlerinden oluşan bulanık bir karar verme sisteminde paralel hesaplamanın tasarlanması ve gerçekleştirimi incelenmiştir. Paralel hesaplama, hesaplamanın en yoğun olduğu BAHS adımında gerçekleştirilmiştir. Önerilen yöntem, homojen ve heterojen bilgisayarlarda ayrı ayrı denenmiş ve sonuçlar tartışılmıştır.

Anahtar Kelimeler

• Bulanık karar verme, Paralel hesaplama, Bulanık analitik hiyerarşi süreci, TOPSIS.

References

1. Flynn, M., “Some computer organizations and their effectiveness”, IEEE Transactions on Computers, 21 (9), 948-960, 1972.
2. Grama A., Gupta A., Karypis G. ve Kumar V., Introduction to Parallel Computing, Addison Wesley Publishing, Newyork, A.B.D., 2003.
3. Gergel, V.P. ve Strongin, R.G., “Parallel computing for globally optimal decision making on cluster systems”, Future Generation Computer Systems, 21 (5), 673-678, 2005.
4. Rahimi, S., Gandy, L. ve Mogharreban, N., “A web-based high-performance multicriteria decision support system for medical diagnosis”, International Journal of Intelligent Systems, 22 (10), 1083-1099, 2007.
5. Wuppalapati, S., Belegundu, A.D., Aziz, A. ve Agarwala, V., “Multicriteria decision making with parallel clusters in structural Engineering Software, 39 (5), 416-421, 2008. Advances in
6. Yamamoto, Y., Nakano, J. ve Fujiwara, T., “Parallel computing in the statistical system Jasp”, Computational Statistics, 25 (2), 291-298, 2009.
7. Zadeh, L.A., “Fuzzy sets”, Information Control, 8, 338-353, 1965.
8. Kahraman, C., Cebeci, U. ve Ruan, D., “Multi-attribute comparison of catering service companies using fuzzy AHP: the case of Turkey”, International Journal of Production Economics, 87, 171-184, 2004.

9. Ertuğrul, İ. ve Karakaşoğlu, N., “Performance evaluation of Turkish cement firms with fuzzy analytic hierarchy process and TOPSIS methods”, Expert Systems with Applications, 36 (1), 702-715, 2009.
10. Chen, G. ve Pham, T.T., Introduction to fuzzy sets, fuzzy logic and fuzzy control systems, CRC Press, New York, A.B.D., 2001.
11. Lin, H.Y., Hsu P.Y. ve Sheen, G.J., “A Fuzzy-Based Decision- Making Procedure for Data Warehouse System Selection”, Expert Systems with Applications, 32 (3), 939-953, 2007.
12. Bellman, R.E. ve Zadeh, L.A.,. “Decision-making in a fuzzy environment”, Management Science, 17 (4), 141-164, 1970.
13. Saaty, T.L., The analytic hierarchy process, McGraw-Hill, A.B.D., 1980.
14. Chang, D.Y., Extent Analysis and Synthetic Decision Optimization Techniques and Applications, World Scientific, Singapore, 1992.
15. Chang, D.Y., “Applications of the extent analysis method on fuzzy AHP”, European Journal of Operational Research, 95, 649-655, 1996.
16. Hwang, C.L. ve Yoon, K., Multiple attributes decision making methods and applications, Springer-Verlag, New York, A.B.D., 1981.
17. Benitez, J.M., Martin, J.C. ve Roman, C., “Using fuzzy number for measuring quality of service in the hotel industry”, Tourism Management, 28 (2), 544-555, 2007.
18. Ballı S. ve Korukoğlu, S., “Operating System Selection Using Fuzzy AHP and TOPSIS Methods”, Mathematical and Computational Applications, 14 (2), 119-130, 2009.
19. Ballı S., Melez Zeki Karar Destek Sistemlerinin Tasarımı ve Gerçekleştirimi, Doktora Tezi, Ege Üniversitesi, İzmir, 2010.
20. Karasulu, B., Ballı, S., Korukoğlu, S. ve Uğur, A., “Kutup Dengeleme Problemi İçin Yüksek Başarımlı Bir Optimizasyon Mühendislik Bilimleri Dergisi, 14 (2), 175-183, 2008.
21. Amdahl, G.M., “Validity of single-processor approach to achieving large-scale computing capability”, Proceedings of AFIPS Conference, Reston, VA., 1967, 483-485.
22. El-Rewini H. ve Abd-El-Barr M., Advanced Computer Architecture and Parallel Processing, JohnWiley and Sons, New York, A.B.D., 2005.