Skip to main content
SpringerLink
Log in

Parameter Estimation of Fuzzy Linear Regression Utilizing Fuzzy Arithmetic and Fuzzy Inverse Matrix

  • Chapter
  • First Online:
Algorithms as a Basis of Modern Applied Mathematics

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 404))

Abstract

The parameter estimation methods of fuzzy linear regression available in the literature have adapted several techniques ranging from mathematical programming to fuzzy least squares which is based on distance notion. Therefore, the literature is vast. However, researchers still try to look for a method that is expected to have estimated spreads as small as possible and good predictions. Each parameter estimation method proposed in the literature has treated fuzzy numbers based on how it implements the data. Namely, the proposed methods somehow restrict the usage of the fuzzy data. In this chapter, a novel method consisting of new notions and calculation procedures is proposed in order to find the parameter estimates of fuzzy linear regression.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bargiela, A., Pedrycz, W., Nakashima, T.: Multiple regression with fuzzy data. Fuzzy Sets Syst. 158(19), 2169–2188 (2007)

    Article  MathSciNet  Google Scholar 

  2. Basaran, M.A.: Calculating fuzzy inverse matrix using fuzzy linear equation system. Appl. Soft Comput. 12, 1810–1813 (2012)

    Article  Google Scholar 

  3. Bekesiene, S., Hoskova-Mayerova, S., Diliunas, P.: Structural equation modeling using the amos and regression of effective organizational commitment indicators in Lithuanian military forces. In: APLIMAT 2017, pp. 91–103. STU, Bratislava (2017). ISBN: 978-1-5108-3698-3

    Google Scholar 

  4. Bekesiene, S., Hoskova-Mayerova, S.: Automatic model building for binary logistic regression by using SPSS 20 software. In: APLIMAT 2019, pp. 31–41. STU, Bratislava (2019). ISBN: 9781510882140

    Google Scholar 

  5. Buckley, J.J., Qu, Y.: Solving systems of linear equations. Fuzzy Sets Syst. 43, 22–32 (1991)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Chen, L.H., Hsueh, C.C.: Fuzzy regression models using the least-squares method based on the concept of distance. IEEE Trans. Fuzzy Syst. 17, 1259–1272 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Dehngan, M., Hashemi, B., Ghatee, M.: Computational methods for solving fully fuzzy linear systems. Appl. Math. Comput. 179, 328–343 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Dehghan, M., Hashemi, B.: Solution of the fully fuzzy linear equations using the decomposition procedure. Appl. Math. Comput. 182, 1568–1580 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Diamond, P.: Fuzzy least squares. Inform. Sci. 46, 141–157 (1988)

    Article  MathSciNet  Google Scholar 

  12. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Application. Academic Press, New York (1980)

    MATH  Google Scholar 

  13. D’Urso, P.: Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput. Stat. Data. Anal. 42(1–2), 47–72 (2003)

    Article  MathSciNet  Google Scholar 

  14. Friedman, M., Ming, M., Kandel, A.: Duality in fuzzy linear systems. Fuzzy Sets Syst. 109, 55–58 (2000)

    Article  MathSciNet  Google Scholar 

  15. Gao, J.: A unified iterative scheme for solving fully fuzzy linear system. Global Congr. Intell. Syst. 1, 431–435 (2009)

    Google Scholar 

  16. Kelkinnama, M., Taheri, S.M.: Fuzzy least-absolutes regression using shape preserving operations. Inform. Sci. 214, 105–120 (2012)

    Article  MathSciNet  Google Scholar 

  17. Liu, H.K.: On the solution of fully fuzzy linear systems. World Acad. Sci. Eng. Math. Comp. Sci. 6, 29–33 (2010)

    MathSciNet  Google Scholar 

  18. Nasseri, S.H., Zahmatkesh, F.: Huang method for solving fully fuzzy linear system of equations. J. Math. Comput. Sci. 1, 1–5 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Yang, M.-S., Lin, T.-S.: Fuzzy least-squares linear regression analysis for fuzzy input–output data. Fuzzy Sets Syst. 126, 389–399 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Engineering, Alanya Alaaddin Keykubat University, Antalya, Turkey

    Murat Alper Basaran

  2. Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Piazza Guerrazzi, 82100, Benevento, Italy

    Biagio Simonetti

  3. The University of Gdansk, Gdansk, Poland

    Biagio Simonetti

Authors
  1. Murat Alper Basaran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Biagio Simonetti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Murat Alper Basaran .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic

    Šárka Hošková-Mayerová

  2. Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania

    Cristina Flaut

  3. Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”, Caserta, Italy

    Fabrizio Maturo

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Basaran, M.A., Simonetti, B. (2021). Parameter Estimation of Fuzzy Linear Regression Utilizing Fuzzy Arithmetic and Fuzzy Inverse Matrix. In: Hošková-Mayerová, Š., Flaut, C., Maturo, F. (eds) Algorithms as a Basis of Modern Applied Mathematics. Studies in Fuzziness and Soft Computing, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-61334-1_21

Download citation

Publish with us

Policies and ethics

Search

Navigation