Meta fuzzy index functions

Abstract

Meta-analysis was introduced to aggregate the findings of different primary studies in statistical aspects. However, in the proposed study, the term "meta" is used to aggregate different models for a specific topic with the help of fuzzy c-means clustering method. One of the motivations of the proposed method is based on the concept of indices. In the literature, there are numerous proposed indices under different conditions for a specific purpose. Our assumption is that each index has some information for a given dataset. Therefore, meta fuzzy index functions, which include each index in each function with a certain degree of membership value, are introduced in the proposed method. Currency crisis and process capability indices are chosen as applications in order to show that the proposed method can be useful tool in terms of indices.

Keywords

• Fuzzy C-means,process capability index,currency crisis index

References

1. Alvarez-Plata, P. and Schrooten, M., The Argentinean Currency Crisis: A Markov Switching Model Estimation, The Developing Economies, XLIV-1 (2006), 79-91.
2. Ari, A. and Cergibozan, R. , A Comparison of Currency Crisis Dating Methods: Turkey 1990-2014, Montenegrin Journal of Economics, 12(3) (2016), 19-37.
3. Bezdek, J.C., Ehrlich, R. and Full, W., FCM: The fuzzy c-means clustering algorithm, Computers and Geosciences, 10(2-3) (1984), 191-203.
4. Bussiere, M. and Fratzscher, M., Towards a new early warning system of financial crises, Journal of International Money and Finance, 25(6) (2006), 953-973.
5. Boyles, R.A., The Taguchi capability index, Journal of Quality Technology, 23(3) (1994), 615-643.
6. Bunda, I. and CaZorzi, M., Signals from housing and lending booms, Emerging Markets Review, 11(1) (2010), 1-20.
7. Chan, L.K., Cheng, S.W., and Spriring FA , A new measure of process capability, Journal of Quality Technology, 20(3) (1988), 162-175.
8. Chen, K.S., Pearn, W.L. and Lin, P.C., A new generalization of the capability index Cm for asymmetric tolerances, International Journal of Reliability, Quality and Safety Engineering, 6(4) (1999), 383-398.

9. Clements, J.A., Process capability calculations for non-normal distributions, Quality Progress, September, (1989), 95-100.
10. Corsetti, G., Pesenti, P., and Roubini, N., What caused the Asian currency and financial crisis?, Japan and the World Economy, 11 (1999), 305-373.
11. Corsetti, G., Pesenti, P., and Roubini, N., Fundamental determinants of the Asian crisis: The role of financial fragility and external imbalances, Regional and Global Capital Flows: Macroeconomic Causes and Consequences, 10 (2001), 11-41.
12. DerSimonian, R. and Laird, N., Meta-analysis in clinical trials, Controlled Clinical Trials, 3 (1986), 177-188.
13. Dunn, J.C., A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of Cybernetics, 3(3) (1973), 32-57.
14. Efron, B., Bootstrap methods: another look at the jackknife, In Breakthroughs in statistics (pp. 569-593). Springer, New York, NY 1992.
15. Eichengreen, B., Rose, A.K., and Wyplosz, C., Contagious currency crises, Scandinavian Journal of Economics, 98(4) (1996), 463-484.
16. Glass, G.V., Primary, secondary, and meta-analysis of research, Educational researcher, 5(10) (1976), 3-8.
17. Johansen, S., Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12(2-3) (1988), 231-254.
18. Kaminsky, G., Lizondo, S. and Reinhart, C.M., Leading Indicators of Currency Crises, IMF Staff Papers, 5(1), (1998) 1-48.
19. Kane, V.E., Process capability indices, Journal of Quality Technology, 18(1) (1986), 41-52.
20. Krishnapuram, R. and Keller, J.M., A possibilistic approach to clustering, IEEE Transactions on Fuzzy Systems,1(2) (1993), 98-110.
21. Krkoska, L., Assessing macroeconomic vulnerability in central Europe, European Bank for Reconstruction and Development ,Working paper, 52 (2000).
22. Pal, N.R., Pal, K., Keller, J.M. and Bezdek, J.C., A possibilistic fuzzy c-means clustering algorithm, IEEE Transactions on Fuzzy Systems, 13(4) (2005), 517-530.
23. Pearn, W.L. and Chen, K.S., Estimating process capability indices for non-normal Pearsonian populations, Quality and Reliability Engineering International, 11(5) (1995), 386-388.
24. Pearn, W.L. and Chen, K.S., Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing, Microelectronics and Reliability, 37(12) (1997), 1853-1858.
25. Pearn, W.L. and Kotz, S., Encyclopedia and Handbook of Process Capability Indices A Comprehensive Exposition Of Quality Control Measures, Singapore: World Scientific Publishing Co. Pte. Ltd. 2006.
26. Sullivan, L.P., Reducing Variability: A New Approach to Quality, Quality Progress, 17(7) (1984), 15-21.
27. Türkiye Cumhuriyet Merkez Bankası (TCMB), https://evds2.tcmb.gov.tr/index.php?/ evds/serieMarket/ (accessed 12.09.207)
28. Wright, P.A., A process capability index sensitive to skewness, Journal of Statistical Computation and Simulation, 52 (1995), 195-203.
29. Von Hagen, J. and Ho, T., Twin Crises: A Reexamination of Empirical Links, Center for European Integration Studies, University of Bonn, 2003.
30. Yalçın, E.C., Süreç verilerinin normal dağılışa uymadığı durumlarda kullanılan süreç yetenek analizi yöntemleri üzerine bir araştırma, Doktora Tezi, Dokuz Eylül University.
31. Yiu, M.S., Ho, A. and Jin, L., Econometric Approach to Early Warnings of Vulnerability in The Banking System and Currency Markets for Hong Kong and Other EMEAP Economies, Hong Kong Monetary Authority, Working Paper, 8 (2009).
32. Zadeh, L.A., Fuzzy sets, Information and control, 8(3) (1965), 338-353.