An amalgamation of crisp and fuzzy quantile regression model

Year 2024, Volume: 42 Issue: 1, 1 - 10, 27.02.2024

Saima Mustafa Hina Basharat Ali Akgul Mohsin Shahzad Abdelhamied Farrag Sayed

Abstract

Fuzzy set theory is the most powerful tool to describe the process of uncertainty which exist in real world and fuzzy regression is an important research topic which can be used for predic-tion by establishing the functional relationship between fuzzy variables. Quantile regression is also a significant statistical method for estimating and drawing inferences about conditional quantile functions. This study introduced the idea of quantile regression with respect to fuzzy. The ordinary fuzzy regression is based on least square method but here we have introduced the idea of weighted least absolute deviation method in fuzzy regression. We have considered two different cases for the illustration of our proposed technique, firstly when the input and output are taken as fuzzy and secondly, the input and output are taken as fuzzy but the param-eters are crisp. The algorithm for each case is based on linear programming problem (LPP). The LPP is constructed for individual case and solved it by the method of Simplex procedure. The proposed work is then compared with the conventional fuzzy regression by using AIC criterion. Empirical study shows that the proposed technique works best in every situation where the fuzzy regression fails and also provide the results in depth.

Keywords

Fuzzy Regression, Quantile Regression, Fuzzy Data, Linear Programming, Simplex Procedure

References

• REFERENCES
• [1] Menger K. Probabilistic theories of relations. Proc Natl Acad Sci U S A 1951;37:178185. [CrossRef]
• [2] Zadeh LA. Fuzzy sets. Inf Control 1965;8:338353. [CrossRef]
• [3] Viertl R. Statistical methods for fuzzy data. Hoboken, New Jersey: John Wiley and Sons; 2011. p. 15. [CrossRef]
• [4] Li J, Zeng W. A new fuzzy regression model based on least absolute deviation. Eng Appl Artif Intell 2016;52:5464. [CrossRef]
• [5] Otadi M. Fully fuzzy polynomial regression with fuzzy neural networks. Neurocomputing 2014;142:486493. [CrossRef]
• [6] Choi SH. Fuzzy regression using least absolute deviation estimators. Soft Comput 2008;12:257263. [CrossRef]
• [7] Tian Y, Zhu Q. Estimation of linear composite quantile regression using EM algorithm. Stat Probab Lett 2016;117:183191. [CrossRef]
• [8] Das P, Ghosal S. Bayesian quantile regression using random B-spline series prior. arXiv 2016:90101.
• [9] Kim J, Kim DH, Choi SH. Least absolute deviation estimator in fuzzy regression. J Appl Math Comput 2005;18:649656. [CrossRef]
• [10] D'Urso P. Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput Stat Data Anal 2003;42:4772. [CrossRef]
• [11] Tanaka H, Guo P. Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst 2000;119:149160.
• [12] Rasheed S, Mustafa S. Regression analysis by using spline techniques (Dissertation Thesis). Islamabad, Pakistan: PMAS Arid Agriculture University; 2013.
• [13] Khalid A, Mustafa S. Flexible smoothing of quantile regression models with B spline and penalties (Dissertation Thesis). Islamabad, Pakistan PMAS Arid Agriculture University Rawalpindi; 2015.
• [14] Yu L, Stander J. Quantile regression: applications and current research areas. J R Stat Soc 2003;52:331350. [CrossRef]
• [15] Baum CF. Quantile regression (presentation). Boston College; 2013. p. 120.
• [16] Kim B, Bishu RR. Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 1998;100:342352. [CrossRef]
• [17] Chung HW. Linear regression analysis for fuzzy input and output data using the extension principle. Comput Math Appl 2003;45:18491859. [CrossRef]