International Journal of Fuzzy Logic and Intelligent Systems

  • 제8권4호
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  • Pages.306-311
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  • 2008
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  • 1598-2645(pISSN)
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  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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Relationship Among h Value, Membership Function, and Spread in Fuzzy Linear Regression using Shape-preserving Operations

  • 발행 : 2008.12.01
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초록

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.

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참고문헌

  1. Bardossy, Note on fuzzy regression, Fuzzy Sets and Systems 37 (1990) 65-75 https://doi.org/10.1016/0165-0114(90)90064-D
  2. Bardossy, I. Bogardi and L. Duckstein, Fuzzy regression in hydrology, Water Resources Research 26(7) (July 1990) 1497-1508 https://doi.org/10.1029/WR026i007p01497
  3. Bardossy, I. Bogardi and W. Kelly, Fuzzy regression for electrical resistivity-Hydraulic conductivity relationships, in:J.Chameau and J.T.P. Yao, Eds, Proc. North American Fuzzy Information Processing Society Workshop (1987) 333-352
  4. Gharpuray, H. Tanaka, L. Fan and F. Lai, Fuzzy linear regressionan alysis of cellulose hydrolysis, Chem. Eng. Commum. 41(1986) 299-314 https://doi.org/10.1080/00986448608911727
  5. Hayashi and H. Tanaka, The fuzzy GMDH algorithm by possibility models and it sapplication, Fuzzy Sets and System 36 (1990) 245-258 https://doi.org/10.1016/0165-0114(90)90182-6
  6. H. Hong, S Lee and H. Y. Do, Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations, Fuzzy Sets and Systems 122 (2001) 513-526 https://doi.org/10.1016/S0165-0114(00)00003-8
  7. H. Hong, Shape preserving multiplications of fuzzy numbers, Fuzzy Sets and Systems 123(2001) 81-84 https://doi.org/10.1016/S0165-0114(00)00107-X
  8. Moskowitz and K. Kim, On assessing the Hvalue in fuzzy linear regression, Fuzzy Sets and Systems 58(1993) 303-327 https://doi.org/10.1016/0165-0114(93)90505-C
  9. Oh, W. Kim and J. Lee, An approach to causal modelling in fuzzy environment and its application, Fuzzy Sets and Systems 35(1990) 43-55 https://doi.org/10.1016/0165-0114(90)90017-Z
  10. Suzuki, K. Furukawa, Y. Inoue and K. Nakagawa, A proposal of rock mass classification for tunnels by the fuzzy regression model, Jap. J. Civi lEng. 418(June 1990)181-190
  11. Tanaka, Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems 24(1987) 363-375 https://doi.org/10.1016/0165-0114(87)90033-9
  12. Tanaka, S. Uejima and K. Asai, Linear regression analysis with fuzzy model, IEEE Transactions on Systems, Man, and Cybernetics SMC-12 (1982) 903-907
  13. Tanaka and J. Watada, Possibilistic linear systems and their applications to the linear regression model, Fuzzy Sets and Systems 27(1988) 275-289 https://doi.org/10.1016/0165-0114(88)90054-1
  14. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inf. Sci. 8 (1975) 199-249 https://doi.org/10.1016/0020-0255(75)90036-5