Least square regression in intuitionistic fuzzy environment with crisp coefficients with the ability to determine the decision level

Document Type : Original Scientific Paper

Authors

1 Behbahan Khatam Alanbia university of Technology

2 Department of Mathematics and Statistics‎, ‎Behbahan Khatam Alanbia University of Technology‎, ‎Khouzestan‎, ‎Iran

Abstract

In practical problems where imprecise components are an inseparable part of them, using fuzzy sets to check their features and measure their efficiency solves some of the current limitations. In this article, we examine the problem of linear regression in an intuitionistic fuzzy environment. Here, we consider the input and output data as intuitionistic fuzzy numbers and assume that the coefficients of the model are crisp numbers. Since to correctly determine the coefficients, we need to calculate the distance between the output of the model and the output data, we present a new parametric distance to calculate the distance between intuitionistic fuzzy numbers. The salient point in this article is that the researcher can estimate the parameter values of the model based on different decision-making levels. To show the efficiency and test the proposed method, several examples are presented at the end of the article. The results are calculated and compared based on the values of different levels of decision-making.

Keywords

Main Subjects

References

Arefi, M. and Taheri, S.M. (2014). Least-squares regression based on Atanassov's intuitionistic fuzzy inputs-outputs and Atanassov's intuitionistic fuzzy parameters. IEEE Transactions on Fuzzy Systems, 23(4):1142–1154.
Choi, S.H., Jung, H.Y. and Kim, H. (2019). Ridge fuzzy regression model. International Journal of Fuzzy Systems, 21(7):2077–2090.
Chakravarty, S., Demirhan, H. and Baser, F. (2022). Modified fuzzy regression functions with a noise cluster against outlier contamination. Expert Systems with Applications, 205:117717.
Chen, T.Y. (2007). A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 158(22):2523–2525.
Chen, C. and Deng, X. (2020). Several new results based on the study of distance measures of intuitionistic fuzzy sets. Iranian Journal of Fuzzy Systems, 17(2):147–163.
Egrioglu, E. and Bas, E. (2023). Robust intuitionistic fuzzy regression functions approaches. Information Sciences, 638:118992.
Garg, H. and Rani, D. (2021). Novel similarity measure based on the transformed right-angled triangles between intuitionistic fuzzy sets and its applications. Cognitive Computation, 13(2):447–465.
Grzegorzewski, P. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 148(2):319–328.
Hazarika, B.B., Gupta, D. and Borah, P. (2021). An intuitionistic fuzzy kernel ridge regression classifier for binary classification. Applied Soft Computing, 112:107816.
Hatzimichailidis, A.G., Papakostas, G.A. and Kaburlasos, V.G. (2012). A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. International Journal of Intelligent Systems, 27(4):396–409.
Hesamian, G., Akbari, M.G. and Roozbeh, M. (2020). Intuitionistic fuzzy partial logistic regression model using ridge methodology. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 28(04):527–543.
Hesamian, G. and Akbari, M.G. (2017). Semi-parametric partially logistic regression model with exact inputs and intuitionistic fuzzy outputs. Applied Soft Computing, 58:517–526.
Hesamian, G. and Akbari, M.G. (2023). A fuzzy Bayesian regression model with Gaussian process prior based on exact predictors and fuzzy responses. Artificial Intelligence Review, 56(11):13765–13785.
Hesamian, G., Johannssen, A. and Chukhrova, N. (2024). An explainable fused lasso regression model for handling high-dimensional fuzzy data. Journal of Computational and Applied Mathematics, 441:115721.
Hung, W.L. and Yang, M.S. (2007). Similarity measures of intuitionistic fuzzy sets based on Lp metric. International Journal of Approximate Reasoning, 46(1):120–136.
Hung, W.L. and Yang, M.S. (2008). On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition. Information Sciences, 178(6):1641–1650.
Jiang, Q., Jin, X., Lee, S.J. and Yao, S. (2019). A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Systems with Applications, 116:439–453.
Khasanzoda, N., Zicmane, I., Beryozkina, S., Safaraliev, M., Sultonov, S. and Kirgizov, A. (2022). Regression model for predicting the speed of wind flows for energy needs based on fuzzy logic. Renewable Energy, 191:723–731.
Leski, J.M. (2023). Fuzzy double-ordered c-regression models based on fuzzy S-estimators. Fuzzy Sets and Systems, 465:108531.
Li, J., Zeng, W., Xie, J. and Yin, Q. (2016). A new fuzzy regression model based on least absolute deviation. Engineering Applications of Artificial Intelligence, 52:54–64.
Ma, M., Friedman, M. and Kandel, A. (1999). A new fuzzy arithmetic. Fuzzy Sets and Systems, 108(1):83–90.
Mahanta, J. and Panda, S. (2021). A novel distance measure for intuitionistic fuzzy sets with diverse applications. International Journal of Intelligent Systems, 36(2):615–627.
Nguyen, R., Singh, S.K. and Rai, R. (2023). FuzzyGAN: Fuzzy generative adversarial networks for regression tasks. Neurocomputing, 525:88–110.
Pang, Y., Shi, M., Zhang, L., Song, X. and Sun, W. (2022). PR-FCM: A polynomial regression-based fuzzy C-means algorithm for attribute-associated data. Information Sciences, 585:209–231.
Sakawa, M. and Yano, H. (1992). Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets and Systems, 47(2):173–181.
Szmidt, E. and Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114(3):505–518.
Yang, Y. and Chiclana, F. (2012). Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Systems with Applications, 39(10):8665–8670.
Wang, W. and Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters, 26(13):2063–2069.
Journal of Statistical Modelling: Theory and Applications
Volume 4, Issue 2
July 2023
Pages 17-34

Files

History

  • Receive Date: 04 February 2024
  • Revise Date: 20 April 2024
  • Accept Date: 22 May 2024

Share

How to cite

Statistics