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An adaptive fuzzy semi-parametric regression model using TPB and ABC-BPNN

  • Fuzzy systems and their mathematics
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Abstract

In this paper, a new hybrid method is developed that incorporates the rationale of truncated power basis (TPB) and artificial bee colony-back propagation neural networks (ABC-BPNN) into an adaptive fuzzy semi-parametric regression model yielding more accurate results and better generalization ability. The proposed adaptive fuzzy semi-parametric regression model comprises sub-model formulation and approximates the observed fuzzy outputs from the outside employing neural networks computation, such that the proposed adaptive fuzzy regression model better explains the inherent dependence and vagueness that exist in a given dataset. Using the cross-validation criterion and absolute deviation-based distance measures for LR-type fuzzy numbers, a target function optimization problem of constructing the adaptive fuzzy semi-parametric regression is performed by solving the smooth function, bandwidth of kernel function, and regression coefficients. This strategy significantly increases the goodness of fit for the proposed algorithm and offers a dependence framework among magnitude and uncertainty for the fuzzy regression model. We also use three formula measures to evaluate the fit quality of the regression results within each membership function as well as in the center or spread tendency property, respectively. The proposed algorithm is numerically evaluated on three experimental examples including a simulation study and two practical cases to prove its practicality and efficiency. Comparative analyses of our proposed method are provided to support its cogency, and the results show that our proposed model is more effective and stable than some other existing fuzzy regressions.

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References

  • Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610

    Google Scholar 

  • Abu Arqub O, Singh J, Alhodaly M (2023) Adaptation of kernel functions-based approach with Atangana-Baleanu-Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci 46:7807–7834

    MathSciNet  Google Scholar 

  • Abu Arqub O, Singh J, Maayah B, Alhodaly M (2021) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag-Leffler kernel differential operator. Math Methods App Sci 46:7965–7986

    MathSciNet  Google Scholar 

  • Akbari MG, Hesamian G (2019) A partial-robust-ridge-based regression model with fuzzy predictors-responses. J Comput Appl Math 351:290–301

    MathSciNet  MATH  Google Scholar 

  • Akbari MG, Hesamian G (2019) Elastic net oriented to fuzzy semiparametric regression model with fuzzy explanatory variables and fuzzy responses. IEEE Trans Fuzzy Syst 27:2433–2442

    Google Scholar 

  • Alex R (2004) Fuzzy normal regression model and related neural networks. Soft Comput 8:717–721

    MATH  Google Scholar 

  • Alshammari M, Al-Smadi M, Abu Arqub O, Hashim I, Almie Alias M (2020) Residual series representation algorithm for solving fuzzy duffing oscillator equations. Symmetry 12:572

    Google Scholar 

  • Asadollahfardi G, Afsharnasab M, Rasoulifard MH, Jebeli MT (2022) Predicting of acid red 14 removals from synthetic wastewater in the advanced oxidation process using artificial neural networks and fuzzy regression. Rendiconti Lincei. Scienze Fisiche e Naturali 33:115–126

    Google Scholar 

  • Cai ZW (2001) Weighted Nadaraya-Watson regression estimation. Stat Probability Lett 51:307–318

    MathSciNet  MATH  Google Scholar 

  • Celmiņš A (1987) Multidimensional least-squares fitting of fuzzy models. Math Model 9:669–690

    MATH  Google Scholar 

  • Chachi J (2018) A weighted least squares fuzzy regression for crisp input-fuzzy output data. IEEE Trans Fuzzy Syst 27:739–748

    Google Scholar 

  • Chachi J, Taheri SM (2016) Multiple fuzzy regression model for fuzzy input-output data. Iran J Fuzzy Syst 13:63–78

    MathSciNet  MATH  Google Scholar 

  • Chachi J, Taheri SM, Arghami NR (2014) A hybrid fuzzy regression model and its application in hydrology engineering. Appl Soft Comput 25:149–158

    Google Scholar 

  • Chachi J, Taheri SM, Pazhand HR (2016) Suspended load estimation using \( L_{1} \)-fuzzy regression, \( L_{2} \)-fuzzy regression and MARS-fuzzy regression models. Hydrol Sci J 61:1489–1502

    Google Scholar 

  • Chang PT, Lee ES (1996) A generalized fuzzy weighted least-squares regression. Fuzzy Sets Syst 82:289–298

    MathSciNet  MATH  Google Scholar 

  • Chen FN, Chen YZ, Zhou J, Liu YY (2016) Optimizing \( h \) value for fuzzy linear regression with asymmetric triangular fuzzy coefficients. Eng Appl Artificial Intell 47:16–24

    Google Scholar 

  • Chen LH, Hsueh CC (2007) A mathematical programming method for formulating a fuzzy regression model based on distance criterion. IEEE Transactions on Systems, Man, and Cybernetics. Part B (Cybernetics) 37:705–712

    Google Scholar 

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

    Google Scholar 

  • Chen LH, Nien SH (2020) A new approach to formulate fuzzy regression models. Appl Soft Comput 86:105915

    Google Scholar 

  • Chen SY, Fang GH, Huang XF, Zhang YH (2018) Water quality prediction model of a water diversion project based on the improved artificial bee colony-backpropagation neural network. Water 10:806

    Google Scholar 

  • Cheng CB, Lee ES (1999) Applying fuzzy adaptive network to fuzzy regression analysis. Comput Math Appl 38:123–140

    MathSciNet  MATH  Google Scholar 

  • Cheng CB, Lee ES (1999) Nonparametric fuzzy regression-k-NN and kernel smoothing techniques. Comput Math Appl 38:239–251

    MathSciNet  MATH  Google Scholar 

  • Choi SH, Buckley JJ (2008) Fuzzy regression using least absolute deviation estimators. Soft Comput 12:257–263

    Google Scholar 

  • Choi SH, Yoon JH (2018) Fuzzy regression based on non-parametric methods. Wseas Trans Syst Control 13:20–25

    Google Scholar 

  • de Andrés-Sánchez J (2017) An empirical assessment of fuzzy Black and Scholes pricing option model in Spanish stock option market. J Intell Fuzzy Syst 33:2509–2521

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Dunyak JP, Wunsch D (2000) Fuzzy regression by fuzzy number neural networks. Fuzzy Sets Syst 112:371–380

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • D’Urso P, Gastaldi T (2002) An “orderwise’’ polynomial regression procedure for fuzzy data. Fuzzy Sets Syst 130:1–19

    MathSciNet  MATH  Google Scholar 

  • Farnoosh R, Ghasemian J, Solaymani FO (2012) A modification on ridge estimation for fuzzy nonparametric regression. Iran J Fuzzy Syst 9:75–88

    MathSciNet  MATH  Google Scholar 

  • Gao YF, Lu QJ (2018) A fuzzy logistic regression model based on the least squares estimation. Comput Appl Math 37:3562–3579

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • He YL, Wang XZ, Huang JZ (2016) Fuzzy nonlinear regression analysis using a random weight network. Inform Sci 364:222–240

    MATH  Google Scholar 

  • He YL, Wei CH, Long H, Ashfaq RAR, Huang JZ (2018) Random weight network-based fuzzy nonlinear regression for trapezoidal fuzzy number data. Appl Soft Comput 70:959–979

    Google Scholar 

  • Hesamian G, Akbari MG (2020) A fuzzy additive regression model with exact predictors and fuzzy responses. Appl Soft Comput 95:106507

    MATH  Google Scholar 

  • Hesamian G, Akbari MG (2020) Fuzzy spline univariate regression with exact predictors and fuzzy responses. J Comput Appl Math 375:112803

    MathSciNet  MATH  Google Scholar 

  • Hesamian G, Akbari MG, Asadollahi M (2017) Fuzzy semi-parametric partially linear model with fuzzy inputs and fuzzy outputs. Expert Syst Appl 71:230–239

    Google Scholar 

  • Hesamian G, Akbari MG, Shams M (2021) Parameter estimation in fuzzy partial univariate linear regression model with non-fuzzy inputs and triangular fuzzy outputs. Iran J Fuzzy Syst 18:51–64

    MathSciNet  MATH  Google Scholar 

  • Hesamian G, Akbari MG (2021) A fuzzy nonlinear univariate regression model with exact predictors and fuzzy responses. Soft Comput 25:3247–3262

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Ishibuchi H, Tanaka H (1992) Fuzzy regression analysis using neural networks. Fuzzy Sets Syst 50:257–265

    MathSciNet  Google Scholar 

  • Karbasi D, Nazemi A, Rabiei M (2020) A parametric recurrent neural network scheme for solving a class of fuzzy regression models with some real-world applications. Soft Comput 24:11159–11187

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Lee HT, Chen SH (2001) Fuzzy regression model with fuzzy input and output data for manpower forecasting. Fuzzy Sets Syst 119:205–213

    MathSciNet  Google Scholar 

  • Lin JG, Zhuang QY, Huang C (2012) Fuzzy statistical analysis of multiple regression with crisp and fuzzy covariates and applications in analyzing economic data of China. Comput Econ 39:29–49

    MATH  Google Scholar 

  • Liu HT, Wang J, He YL, Ashfaq RAR (2017) Extreme learning machine with fuzzy input and fuzzy output for fuzzy regression. Neural Comput Appl 28:3465–3476

    Google Scholar 

  • Liu J, Meng LZ (2019) Integrating artificial bee colony algorithm and BP neural network for software aging prediction in IoT environment. IEEE Access 7:32941–32948

    Google Scholar 

  • Liu XL, Chen YZ (2013) A systematic approach to optimizing value for fuzzy linear regression with symmetric triangular fuzzy numbers. Math Prob Eng 2013:210164

    MathSciNet  MATH  Google Scholar 

  • Mirzaei F, Delavar M, Alzoubi I, Arrabi BN (2018) Modeling and predict environmental indicators for land leveling using adaptive neuro-fuzzy inference system (ANFIS), and regression. Int J Energy Sector Manag 12:484–506

    Google Scholar 

  • Mosleh M, Otadi M, Abbasbandy S (2013) Evaluation of fuzzy regression models by fuzzy neural network. J Comput Appl Math 234:825–834

    MathSciNet  MATH  Google Scholar 

  • Nasrabadi E, Hashemi SM (2008) Robust fuzzy regression analysis using neural networks. Int J Uncertainty Fuzziness Knowl-Based Syst 16:579–598

    MATH  Google Scholar 

  • Perperoglou A, Sauerbrei W, Abrahamowicz M, Schmid M (2019) A review of spline function procedures in \( R \). BMC Med Res Methodol 19:1–16

    Google Scholar 

  • Petit-Renaud S, Denœux T (2004) Nonparametric regression analysis of uncertain and imprecise data using belief functions. Int J Approx Reason 35:1–28

  • Prakaash AS, Sivakumar K (2021) Optimized recurrent neural network with fuzzy classifier for data prediction using hybrid optimization algorithm:scope towards diverse applications. Int J Wavelets Multiresolution Inform Process 19:2050074

    MathSciNet  MATH  Google Scholar 

  • Rabiei MR, Arashi M, Farrokhi M (2019) Fuzzy ridge regression with fuzzy input and output. Soft Comput 23:12189–12198

  • López Roldán, de Hierro AF, Martinez-Moreno J, Pena CA, López Roldán, de Hierro C (2016) A fuzzy regression approach using Bernstein polynomials for the spreads: computational aspects and applications to economic models. Math Comput Simul 128:13–25

    MathSciNet  MATH  Google Scholar 

  • Salmani F, Taheri SM, Yoon JH, Abadi A, Majd HA, Abbaszadeh A (2017) Logistic regression for fuzzy covariates:modeling, inference, and applications. Int J Fuzzy Syst 19:1635–1644

  • Shen SL, Mei CL, Cui JL (2010) A fuzzy varying coefficient model and its estimation. Comput Math Appl 60:1696–1705

    MathSciNet  MATH  Google Scholar 

  • Spiliotis M, Angelidis P, Papadopoulos B (2020) A hybrid probabilistic bi-sector fuzzy regression based methodology for normal distributed hydrological variable. Evol Syst 11:255–268

    Google Scholar 

  • Taheri SM, Kelkinnama M (2012) Fuzzy linear regression based on least absolutes deviations. Iran J Fuzzy Syst 9:121–140

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Thrane C (2019) Applied regression analysis. Taylor and Francis

    Google Scholar 

  • Tzimopoulos C, Papadopoulos K, Papadopoulosc B (2016) Fuzzy regression with applications in hydrology. Optimization 5:69–75

    Google Scholar 

  • Wang N, Zhang WX, Mei CL (2007) Fuzzy non-parametric regression based on local linear smoothing technique. Inform Sci 177:3882–3900

    MathSciNet  MATH  Google Scholar 

  • Wang Q, Xu ZX, Xu ZJ, Shi YY, Wu HL, Shen GF (2019) PM2. 5 prediction model based on ABC-BP. Int Conf Commun Inform Syst Comput Eng 2019:140–143

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Yen KK, Ghoshray S, Roig G (1999) A linear regression model using triangular fuzzy number coefficients. Fuzzy Sets Syst 106:167–177

    MathSciNet  MATH  Google Scholar 

  • Zeng WY, Feng QL, Li JH (2017) Fuzzy least absolute linear regression. Appl Soft Comput 52:1009–1019

    Google Scholar 

  • Zhang D, Deng LF, Cai KY, So A (2005) Fuzzy nonlinear regression with fuzzified radial basis function network. IEEE Trans Fuzzy Syst 13:742–760

    Google Scholar 

  • Zimmermann HJ (2011) Fuzzy set theory-and its applications. Springer Science & Business Media

Download references

Acknowledgements

The authors are thankful to the referees for their helpful comments.

Funding

This paper work was supported by Priority Discipline Project of Shanghai [Grant No. T0502] and Foundation of Hujiang [Grant No. B14005].

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  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Keli Jiang & Qiujun Lu

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  1. Keli Jiang
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  2. Qiujun Lu
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All authors were contributed to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to Keli Jiang.

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Jiang, K., Lu, Q. An adaptive fuzzy semi-parametric regression model using TPB and ABC-BPNN. Soft Comput 27, 16449–16463 (2023). https://doi.org/10.1007/s00500-023-09191-9

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