Real-time fuzzy regression analysis: a convex hull approach. (English) Zbl 1214.62077
Summary: We present an enhancement of fuzzy regression analysis with regard to its aspect of real-time processing. Let us recall that fuzzy regression generalizes the concept of classical (numeric) regression in the sense of bringing additional capabilities that allow the model to deal with fuzzy (granular) data. We show that a convex hull method provides a useful vehicle to reduce computing time, which becomes of particular relevance in case of real-time data analysis. Our objective is to develop an efficient real-time fuzzy regression analysis based on the use of convex hull, specifically a Beneath-Beyond algorithm. In this algorithm, the re-construction of convex hull edges depends on incoming vertices while a re-computing procedure can be realized in real-time. We demonstrate the use of the developed enhancement to application to unit performance assessment and air pollution data. An important role of convex hull is contrasted with the limitations of linear programming used in the “standard” regression.
MSC:
| 62J86 | Fuzziness, and linear inference and regression |
| 90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |
| 65C60 | Computational problems in statistics (MSC2010) |
| 90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |
| 90C05 | Linear programming |
Software:
QhullReferences:
| [1] | Aldrin, M.; Hobæk, I. H., Generalized additive modeling of air pollution, traffic volume and meteorology, Atmospheric Environment, 39, 11, 2145-2155 (2005) |
| [2] | Aznar, J.; Guijarro, F., Estimating regression parameters with imprecise input data in an appraisal context, European Journal of Operational Research, 176, 3, 1896-1907 (2007) · Zbl 1110.90047 |
| [3] | Barber, B.; Dobkin, D. P.; Hupdanpaa, H., The quickhull algorithm for convex hull, ACM Transaction on Mathematical Software, 22, 4, 469-483 (1996) · Zbl 0884.65145 |
| [4] | Bargiela, A.; Pedrycz, W.; Nakashima, T., Multiple regression with fuzzy data, Fuzzy Sets and Systems, 158, 19, 2169-2188 (2007) · Zbl 1121.62063 |
| [5] | Bohm, C., Kriegel, H-P., 2000. Determining the convex hull in large multidimensional databases. In: International Conference on Data Warehousing and Knowledge Discovery (DaWaK), Munich, Germany, pp. 294-306.; Bohm, C., Kriegel, H-P., 2000. Determining the convex hull in large multidimensional databases. In: International Conference on Data Warehousing and Knowledge Discovery (DaWaK), Munich, Germany, pp. 294-306. · Zbl 0986.68626 |
| [6] | Chang, Y-H. O.; Ayyub, B. M., Fuzzy regression methods-a comparative assessment, Fuzzy Sets and Systems, 119, 2, 187-203 (2001) |
| [7] | Chen, Y., Dong, G., Han, J., Wah, B., Wang, J., 2002. Multidimensional regression analysis of time-series data streams. In: International Very Large Data Bases (VLDB) Conference.; Chen, Y., Dong, G., Han, J., Wah, B., Wang, J., 2002. Multidimensional regression analysis of time-series data streams. In: International Very Large Data Bases (VLDB) Conference. |
| [8] | Dom, R.M., Kareem, S.A., Zain, R., Abidi, B., 2007. An adaptive fuzzy regression model for the prediction of dichotomous response variables. In: IEEE Proceedings of 2007 International Conference on Computational Science and Its Applications, Kuala Lumpur, pp. 14-19.; Dom, R.M., Kareem, S.A., Zain, R., Abidi, B., 2007. An adaptive fuzzy regression model for the prediction of dichotomous response variables. In: IEEE Proceedings of 2007 International Conference on Computational Science and Its Applications, Kuala Lumpur, pp. 14-19. |
| [9] | Donoso, S.; Marin, N.; Vila, M. A., System of possibilistic regression: a case study in ecological inference, Mathware and Soft Computing, 12, 2/3, 169-184 (2005) · Zbl 1093.68647 |
| [10] | D’Urso, P.; Santoro, A., Goodness of fit and variable selection in the fuzzy multiple linear regression, Fuzzy Sets and System, 157, 19, 2627-2647 (2006) · Zbl 1112.62064 |
| [11] | Emiris, Z., A complete implementation for computing general dimensional convex hulls, International Journal of Computing Geometry and Applications, 8, 2, 223-249 (1998) · Zbl 1035.68529 |
| [12] | Gould, P. G.; Koehler, A. B.; Keith Ord, J.; Snyder, R. D.; Hyndman, R. J.; Vahid-Araghi, F., Forecasting time series with multiple seasonal patterns, European Journal of Operational Research, 19, 1, 207-222 (2008) · Zbl 1142.62070 |
| [13] | Guo, P.; Tanaka, H., Decision making with interval probabilities, European Journal of Operational Research, 203, 2, 444-454 (2010) · Zbl 1177.90215 |
| [14] | He, Y.-Q.; Chan, L.-K.; Wu, M.-L., Balancing productivity and consumer satisfaction for profitability: statistical and fuzzy regression analysis, European Journal of Operational Research, 176, 1, 252-263 (2007) · Zbl 1137.91520 |
| [15] | Hoa, P.-Y.; Chiang, J-H., Fuzzy regression analysis by support vector learning approach, IEEE Transactions on Fuzzy Systems, 16, 2, 428-441 (2008) |
| [16] | Hojati, M.; Bector, C. R.; Smimou, K., A simple method for computation of fuzzy linear regression, European Journal of Operational Research, 166, 1, 172-184 (2005) · Zbl 1067.62549 |
| [17] | Hsua, B.-M.; Shub, M.-H., Fuzzy inference to assess manufacturing process capability with imprecise data, European Journal of Operational Research, 186, 2, 652-670 (2008) · Zbl 1138.90381 |
| [18] | Kao, C.; Chyu, C.-L., Least-squares estimates in fuzzy regression analysis, European Journal of Operational Research, 148, 2, 426-435 (2003) · Zbl 1045.62068 |
| [19] | Kumar, P. R.; Ravi, V., Bankruptcy prediction in banks and firms via statistical and intelligent techniques - A review, European Journal of Operational Research, 180, 1, 1-28 (2007) · Zbl 1114.91305 |
| [20] | Korhonen, P.; Syrjänen, M., Resource allocation based on efficiency analysis, Management Science Journal, 50, 8, 1134-1144 (2004) · Zbl 1232.91366 |
| [21] | Levy, J. I.; Bennett, D. H.; Melly, S. J.; Spengler, J. D., Influence of traffic patterns on particulate matter and polycyclic aromatic hydrocarbon concentrations in Roxbury, Massachusetts, Journal of Exposure Analysis and Environmental Epidemiology, 13, 364-371 (2003) |
| [22] | Miller, R.; Stout, Q. F., Efficient parallel convex hull algorithm, IEEE Transaction of Computers, 37, 12, 1605-1618 (1988) · Zbl 0663.68057 |
| [23] | Narula, S. C.; Wellington, J. F., Multiple criteria linear regression, European Journal of Operational Research, 181, 2, 767-772 (2007) · Zbl 1131.62308 |
| [24] | Olafsson, S.; Li, X.; Wu, S., Operations research and data mining, European Journal of Operational Research, 187, 3, 1429-1448 (2008) · Zbl 1137.90776 |
| [25] | Ramli, A.A., Watada, J., 2009. New perspectives of fuzzy performance assessment of manufacturing enterprises. In: The Fifth International Conference on Intelligent Manufacturing & Logistics Systems (IML 2009), Waseda University, Kitakyushu, Japan, 16-18 February.; Ramli, A.A., Watada, J., 2009. New perspectives of fuzzy performance assessment of manufacturing enterprises. In: The Fifth International Conference on Intelligent Manufacturing & Logistics Systems (IML 2009), Waseda University, Kitakyushu, Japan, 16-18 February. |
| [26] | Sakawa, M.; Yano, H., Fuzzy linear regression analysis for fuzzy input-output data, Information Science, 63, 3, 191-206 (1992) · Zbl 0751.62031 |
| [27] | Shapiro, A.F., 2004. Fuzzy regression and the term structure of interest rates revisited. In: 14th International AFIR 2004, Boston, 7-10 November.; Shapiro, A.F., 2004. Fuzzy regression and the term structure of interest rates revisited. In: 14th International AFIR 2004, Boston, 7-10 November. |
| [28] | Stahl, C., A strong consistent least-squares estimator in a linear fuzzy regression model with fuzzy parameters and fuzzy dependent variables, Fuzzy Sets and Systems, 157, 19, 2593-2607 (2006) · Zbl 1099.62072 |
| [29] | Tanaka, H.; Guo, P., Portfolio selections based on upper and lower exponential possibility distributions, European Journal of Operational Research, 114, 1, 115-126 (1999) · Zbl 0945.91017 |
| [30] | Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE Transaction on System, Man and Cybernetics, 12, 6, 903-907 (1982) · Zbl 0501.90060 |
| [31] | Taylor, J. W., A comparison of univariate time series methods for forecasting intraday arrivals at a call center, Management Science Journal, 54, 2, 253-265 (2008) · Zbl 1232.90214 |
| [32] | Wang, H.-F.; Tsaur, R.-C., Insight of a fuzzy regression model, Fuzzy Sets and Systems, 112, 3, 355-369 (2000) · Zbl 0948.62050 |
| [33] | Wang, W.; Chena, S.; Qu, G., Incident detection algorithm based on partial least squares regression, Transportation Research Part C: Emerging Technologies, 16, 1, 54-70 (2008) |
| [34] | Watada, J.; Pedrycz, W., A fuzzy regression approach to acquisition of linguistic rules, (Handbook on Granular Commutation (2008), John Wiley & Sons Ltd), 719-740, Chapter 32 |
| [35] | Watada, J., Toyoura, Y., Hwang, S.G. Convex hull approach to fuzzy regression analysis and its application to oral age model. In: International Fuzzy System Association World Congress and 20th North American Fuzzy Information Processing Society International Conference 2001, Joint Ninth, Canada, 2001, 867-871.; Watada, J., Toyoura, Y., Hwang, S.G. Convex hull approach to fuzzy regression analysis and its application to oral age model. In: International Fuzzy System Association World Congress and 20th North American Fuzzy Information Processing Society International Conference 2001, Joint Ninth, Canada, 2001, 867-871. |
| [36] | Watada, J.; Wang, S.; Pedrycz, W., Building confidence-interval-based fuzzy random regression models, IEEE Transactions on Fuzzy Systems, 17, 6, 1273-1283 (2009) |
| [37] | Wu, C-W., Decision-making in testing process performance with fuzzy data, European Journal of Operational Research, 193, 2, 499-509 (2009) · Zbl 1152.91411 |
| [38] | Yang, M.-S.; Lin, T.-S., Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 126, 3, 389-399 (2002) · Zbl 1006.62055 |
| [39] | Yao, C.-C.; Yu, P.-T., Fuzzy regression based on asymmetric support vector machines, Applied Mathematics and Computation, 182, 1, 175-193 (2006) · Zbl 1113.62084 |
| [40] | Yu, P.-S.; Chena, S.-T.; Changa, I.-F., Support vector regression for real-time flood stage forecasting, Journal of Hydrology, 328, 3-4, 704-716 (2006) |
| [41] | Zadeh, L. A., Making computers think like people, IEEE Spectrum, 21, 8, 26-32 (1984) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
