International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Fuzzy Regression Model Using Trapezoidal Fuzzy Numbers for Re-auction Data

  • Kim, Il Kyu (Department of Real Estate and Finance, Gwangju University) ;
  • Lee, Woo-Joo (Department of Mathematics, Yonsei University) ;
  • Yoon, Jin Hee (School of Mathematics and Statistics, Sejong University) ;
  • Choi, Seung Hoe (School of Liberal Arts and Science, Korea Aerospace University)
  • Received : 2016.01.05
  • Accepted : 2016.03.24
  • Published : 2016.03.25
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Abstract

Re-auction happens when a bid winner defaults on the payment without making second in-line purchase declaration even after determining sales permission. This is a process of selling under the court's authority. Re-auctioning contract price of real estate is largely influenced by the real estate business, real estate value, and the number of bidders. This paper is designed to establish a statistical model that deals with the number of bidders participating especially in apartment re-auctioning. For these, diverse factors are taken into consideration, including ratio of minimum sales value from the point of selling to re-auctioning, number of bidders at the time of selling, investment value of the real estate, and so forth. As an attempt to consider ambiguous and vague factors, this paper presents a comparatively vague concept of real estate and bidders as trapezoid fuzzy number. Two different methods based on the least squares estimation are applied to fuzzy regression model in this paper. The first method is the estimating method applying substitution after obtaining the estimators of regression coefficients, and the other method is to estimate directly from the estimating procedure without substitution. These methods are provided in application for re-auction data, and appropriate performance measure is also provided to compare the accuracies.

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References

  1. P. Klemperer, The Economic Theory of Auctions. Cheltenham, UK: Edward Elgar, 2000.
  2. K. H. Lee, Court Practice Real Estate Auctions. Seoul, Korea: GoodAuction, 2007.
  3. H. J. Yoon, Real Estate Law. Seoul, Korea: Hakmun publishing, 2004.
  4. P. Klemperer, "Auction theory: a guide to the literature," Journal of Economic Surveys, vol. 13, no. 3, pp. 227-286, 1999. http://dx.doi.org/10.1111/1467-6419.00083
  5. L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338-353, 1965. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
  6. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning I," Information Sciences, vol. 8, no. 3, pp. 199-249, 1975. http://dx.doi.org/10.1016/0020-0255(75)90036-5
  7. H. Tanaka and I. Hayashi, "Possibilistic linear regression analysis for fuzzy data," European Journal of Operational Research, vol. 40, no. 3, pp. 389-396, 1989. http://dx.doi.org/10.1016/0377-2217(89)90431-1
  8. H. Tanaka, S. Uejima, and K. Asai, "Linear regression analysis with fuzzy model," IEEE Transactions on Systems, Man, and Cybernetics, vol. 12, no. 6, pp. 903-907, 1982. http://dx.doi.org/10.1109/TSMC.1982.4308925
  9. A. R. Arabpour and M. Tata, "Estimating the parameters of a fuzzy linear regression model," Iranian Journal of Fuzzy Systems, vol. 5, no. 2, pp. 1-19, 2008.
  10. A. Bisserier, R. Boukezzoula, and S. Galichet, "A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals," Information Sciences, vol. 180, no. 19, pp. 3653-3673, 2010. http://dx.doi.org/10.1016/j.ins.2010.06.017
  11. A. Bisserier, R. Boukezzoula, and S. Galichet, "Linear fuzzy regression using trapezoidal fuzzy intervals," Journal of Uncertain Systems, vol. 4, no.1, pp. 59-72, 2010.
  12. C. H. Cheng, J. R. Chang, and C. A. Yeh, "Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost," Technological Forecasting and Social Change, vol. 73, no. 5, pp. 524-542, 2006. http://dx.doi.org/10.1016/j.techfore.2005.07.004
  13. H. Y. Jung, J. H. Yoon, and S. H. Choi, "Fuzzy linear regression using rank transform method," Fuzzy Sets and Systems, vol. 274, pp. 97-108, 2015. http://dx.doi.org/10.1016/j.fss.2014.11.004
  14. H. T. Liu, "An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers," Fuzzy Optimization and Decision Making, vol. 6, no. 1, pp. 63-80, 2007. http://dx.doi.org/10.1007/s10700-006-0025-9
  15. A. Maleki, E. Pasha, and T. Razzaghnia, "Possibility linear regression analysis with trapezoidal fuzzy data," World Applied Sciences Journal, vol. 18, no. 1, pp. 37-42, 2012.
  16. H. Y. Jung, W. J. Lee, and J. H. Yoon, "A unified approach to asymptotic behaviors for the autoregressive model with fuzzy data," Information Sciences, vol. 257, pp. 127-137, 2014. http://dx.doi.org/10.1016/j.ins.2013.09.024
  17. H. K. Kim, J. H. Yoon, and Y. Li, "Asymptotic properties of least squares estimation with fuzzy observations," Information Sciences, vol. 178, no. 2, pp. 439-451, 2008. http://dx.doi.org/10.1016/j.ins.2007.07.010
  18. W. J. Lee, H. Y. Jung, J. H. Yoon, and S. H. Choi, "The statistical inferences of fuzzy regression based on bootstrap techniques," Soft Computing, vol. 19, no. 4, pp. 883-890, 2015. http://dx.doi.org/10.1007/s00500-014-1415-5
  19. R. E. Giachetti and R. E. Young, "A parametric representation of fuzzy numbers and their arithmetic operators,"Fuzzy Sets and Systems, vol. 91, no. 2, pp. 185-202, 1997. http://dx.doi.org/10.1016/S0165-0114(97)00140-1
  20. R. R. Yager, "Using trapezoids for representing granular objects: applications to learning and OWA aggregation," Information Sciences, vol. 178, no. 2, 363-380, 2008. http: //dx.doi.org/10.1016/j.ins.2007.08.015
  21. S. H. Choi and J. J. Buckley, "Fuzzy regression using least absolute deviation estimators," Soft Computing, vol. 12, no. 3, pp. 257-263, 2007. http://dx.doi.org/10.1007/s00500-007-0198-3
  22. A. Kumar, J. Kaur, and P. Singh, "Solving fully fuzzy linear programming problems with inequality constraints," International Journal of Physical and Mathematical Sciences, vol. 1, pp. 6-17, 2010.
  23. S. H. Nasseri, E. Behmanesh, F. Taleshian, M. Abdolalipoor, and N. A. Taghi-Nezhad, "Fully fuzzy linear programming with inequality constraints," International Journal of Industrial Mathematics, vol. 5, no. 4, pp. 309-316, 2013.
  24. J. H. Yoon and S. H. Choi, "Fuzzy least squares estimation with new fuzzy operations," Advances in Intelligent Systems and Computing, vol. 190, pp. 193-202, 2013. http://dx.doi.org/10.1007/978-3-642-33042-1_21
  25. A. K. Shaw and T. K. Roy, "Generalized trapezoidal fuzzy number with its arithmetic operations and its application in fuzzy system reliability analysis," International Journal of Pure and Applied Sciences and Technology, vol. 5, no. 2, pp. 60-76, 2011.
  26. M. S. Sin and N. H. Cho, "Fault tree analysis model based on trapezoidal fuzzy number," Journal of the Korean Society for Quality Management, vol. 20, no. 1, pp. 118-125, 1992.
  27. M. Namdari, J. H. Yoon, A. Abadi, S. M. Taheri, and S. H. Choi, "Fuzzy logistic regression with least absolute deviations estimators," Soft Computing, vol. 19, no. 4, pp. 909-917, 2015. http://dx.doi.org/10.1007/s00500-014-1418-2