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A weighted goal programming approach to fuzzy linear regression with crisp inputs and type-2 fuzzy outputs

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Abstract

Many researches have been carried out in fuzzy linear regression the past three decades. However, almost all of them are limited to type-1 fuzzy data. A fuzzy linear regression model with type-2 fuzzy output data and type-2 fuzzy coefficients is studied in this paper. A linear programming model based on goal programming is proposed to calculate the regression coefficients. To evaluate the proposed model, we present some indices based on the standard deviation, the correlation coefficient, and the standard error of estimate. The proposed method is illustrated by some numerical examples.

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References

  • Celmins A (1987) Least squares model fitting to fuzzy vector data. Fuzzy Sets Syst 22:245–269

    Article  MathSciNet  Google Scholar 

  • Charnes A, Cooper WW (1977) Goal programming and multiple objective optimizations. Eur J Oper Res 1:39–54

    Article  MATH  MathSciNet  Google Scholar 

  • Coppi R, D’Urso P, Giordani P, Santoro A (2006) Least squares estimation of a linear regression model with LR fuzzy response. Comput Stat Data Anal 51:267–286

    Article  MATH  MathSciNet  Google Scholar 

  • Diamond P (1988) Fuzzy least squares. Inf Sci 46:141–157

    Article  MATH  MathSciNet  Google Scholar 

  • Donahue RL, Miller RW, Shickluna JC (1983) Soils, an introduction to soils and plant growth. Prentice-Hall, London

  • D’Urso P (2003) Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput Stat Data Anal 42:47–72

    Article  MATH  MathSciNet  Google Scholar 

  • Hamrawi H, Coupland S (2009) Type-2 fuzzy arithmetic using alpha-planes. In: IFSA international congress on fuzzy systems, Portugal, pp 606–611

  • Hassanpour H, Maleki HR, Yaghoobi MA (2009) A goal programming approach to fuzzy linear regression with non-fuzzy input and fuzzy output data. Asia Pac J Oper Res 26(5):587–604

  • Hassanpour H, Maleki HR, Yaghoobi MA (2010) Fuzzy linear regression model with crisp coefficients: a goal programming approach. Iran J Fuzzy Syst 7(2):19–39

    MATH  MathSciNet  Google Scholar 

  • Hassanpour H, Maleki HR, Yaghoobi MA (2011) A goal programing approach to fuzzy linear regression with fuzzy input–output data. Soft Comput 15:1569–1580

    Article  MATH  Google Scholar 

  • Hisdal E (1981) The IF THEN ELSE statement and interval-valued fuzzy sets of higher type. Int J Man Mach Stud 15:385–455

    Article  MATH  MathSciNet  Google Scholar 

  • Hojati M, Bector CR, Smimou K (2005) A simple method for computation of fuzzy linear regression. Eur J Oper Res 166:172–184

    Article  MATH  MathSciNet  Google Scholar 

  • Hung WL, Yang MS (2006) An omission approach for detecting outliers in fuzzy regression models. Fuzzy Sets Syst 157:3109–3122

    Article  MATH  MathSciNet  Google Scholar 

  • Kao C, Chyu CL (2003) Least-squares estimates in fuzzy regression analysis. EJOR 148:426–435

    Article  MATH  MathSciNet  Google Scholar 

  • Kim B, Bishu RR (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 100:343–352

    Article  Google Scholar 

  • Klir GJ, Sentz K (2006) Aspects of automatic text analysis. In: On the issue of linguistic approximation. Springer, New York

  • Maximal Software Inc. (2013) http://www.maximalsoftware.com. Accessed 5 Apr 2013

  • Mendel JM (1999) Computing with words when words can mean different things to different people. in: Presented at international ICSC congress on computational intelligence: methods and applications, 3rd annual symposium on fuzzy logic and applications, Rochester, p 2225

  • Ming M, Friedman M, Kandel A (1997) General fuzzy least-squares. Fuzzy Sets Syst 88:107–118

    Article  MATH  MathSciNet  Google Scholar 

  • Modarres M, Nasrabadi E, Nasrabadi MM (2004) Fuzzy linear regression analysis from the point of view risk. Int J Uncertain Fuzziness Knowl Based Syst 12(5):635–649

    Article  MATH  MathSciNet  Google Scholar 

  • Modarres M, Nasrabadi E, Nasrabadi MM (2005) Fuzzy linear regression models with least square errors. Appl Math Comput 163:977–989

    Article  MATH  MathSciNet  Google Scholar 

  • Mohammadi J, Taheri SM (2004) Pedomodels fitting with fuzzy least squares regression. Iran J Fuzzy Syst 1(2):45–61

    MATH  MathSciNet  Google Scholar 

  • Özelkan EC, Duckstein L (2000) Multi-objective fuzzy regression: a general framework. Comput Oper Res 27:635–652

    Article  MATH  Google Scholar 

  • Peters G (1994) Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst 63:45–55

    Article  Google Scholar 

  • Poleshchuk O, Komarov E (2008) Multiple hybrid regression for fuzzy observed data. In: Fuzzy information processing society (NAFIPS), pp 1–4

  • Poleshchuk O, Komarov E (2011) A nonlinear hybrid fuzzy least-squares regression model. In: Fuzzy information processing society (NAFIPS), pp 1–6

  • Poleshchuk O, Komarov E (2012) A fuzzy linear regression model for interval type-2 fuzzy sets. In: Fuzzy information processing society (NAFIPS), pp 1–5

  • Sakawa M, Yano H (1992) Multiobjective fuzzy linear regression analysis for fuzzy input–output data. Fuzzy Sets Syst 47:173–181

    Article  MATH  Google Scholar 

  • Sakawa M, Yano H (1992) Fuzzy linear regression and its applications. In: Kacprzyk J, Fedrizzi M (eds) Studies in fuzziness. Fuzzy regression analysis, vol 1. Omnitech Press, Warsaw, pp 61–80

  • Savic DA, Pedrycz W (1991) Evaluation of fuzzy linear regression models. Fuzzy SetsSyst 39:51–63

  • Schage L (1999) LINGO release 6.0. LINDO System Inc

  • Tanaka H, Uejima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Man Cybren 12:903–907

    Article  MATH  Google Scholar 

  • Tanaka H (1987) Fuzzy data analysis by possibilistic linear models. Fuzzy Sets Syst 24:363–375

    Article  MATH  Google Scholar 

  • Tanaka H, Hayashi I, Watada J (1989) Possibilistic linear regression analysis for fuzzy data. Eur J Oper Res 40:389–396

    Article  MATH  MathSciNet  Google Scholar 

  • Wünsche A, Näther W (2002) Least-squares fuzzy regression with fuzzy random variables. Fuzzy Sets Syst 130:43–50

    Article  MATH  Google Scholar 

  • Xu R, Li C (2001) Multidimensional least-squares fitting with a fuzzy model. Fuzzy Sets Syst 119:215–223

    Article  MATH  Google Scholar 

  • Yaghoobi MA, Tamiz M (2007) A method for solving fuzzy goal programming problems based on MINMAX approach. Eur J Oper Res 177(3):1580–1590

    Article  MATH  MathSciNet  Google Scholar 

  • Yang MS, Ko CH (1996) On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy sets Syst 84:49–60

    Article  MATH  MathSciNet  Google Scholar 

  • Yang MS, Lin TS (2002) Fuzzy least squares linear regression analysis for fuzzy input-output data. Fuzzy Sets Syst 126:389–399

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1975) Concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Islamic Republic of Iran

    E. Hosseinzadeh & H. Hassanpour

  2. Department of Statistics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Islamic Republic of Iran

    M. Arefi

Authors
  1. E. Hosseinzadeh
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  2. H. Hassanpour
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  3. M. Arefi
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Corresponding author

Correspondence to E. Hosseinzadeh.

Additional information

Communicated by V. Loia.

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Hosseinzadeh, E., Hassanpour, H. & Arefi, M. A weighted goal programming approach to fuzzy linear regression with crisp inputs and type-2 fuzzy outputs. Soft Comput 19, 1143–1151 (2015). https://doi.org/10.1007/s00500-014-1328-3

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