nach oben

Soft Computing

Erschienen in:

06.06.2020 | Foundations

A parametric recurrent neural network scheme for solving a class of fuzzy regression models with some real-world applications

verfasst von: Delara Karbasi, Alireza Nazemi, Mohammadreza Rabiei

Erschienen in: Soft Computing | Ausgabe 15/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, a hybrid scheme based on recurrent neural networks for approximate fuzzy coefficients (parameters) of fuzzy linear and polynomial regression models with fuzzy output and crisp inputs is presented. Here, a neural network is first constructed based on some concepts of convex optimization and stability theory. The suggested neural network model guarantees to find the approximate parameters of the fuzzy regression problem. The existence and convergence of the trajectories of the neural network are studied. The Lyapunov stability for the neural network is also shown. Some illustrative examples provide a further demonstration of the effectiveness of the method.

Vorheriger Artikel Western culture correct guidance and penetration teaching and its multi-dimensional training mode

Nächster Artikel Study on Green’s relations in ordered semihypergroups

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Abbasbandy S, Otadi M (2006) Numerical solution of fuzzy polynomials by fuzzy neural network. Appl Math Comput 181:1084–1089MathSciNetMATH

Akbari MG, Hesamian G (2017) Linear model with exact inputs and interval-valued fuzzy outputs. IEEE Trans Fuzzy Syst 26:518–530

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

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

Arefi M (2020) Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters. Soft Comput 24:311–320

Arjmandzadeh Z, Safi MR, Nazemi AR (2017) A new neural network model for solving random interval linear programming problems. Neural Netw 89:11–18MATH

Avriel M (2003) Nonlinear programming: analysis and methods. Courier Corporation, ChelmsfordMATH

Azadeh A, Saberi M, Seraj O (2010) An integrated fuzzy regression algorithm for energy consumption estimation with non-stationary data: a case study of Iran. Energy 35:2351–2366

Azadeh A, Saberi M, Gitiforouz A (2011) An integrated simulation-based fuzzy regression-time series algorithm for electricity consumption estimation with non-stationary data. J Chin Inst Engineers 34:1047–1066

Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley, New YorkMATH

Buckley JJ, Eslami E (1997) Neural net solutions to fuzzy problems: the quadratic equation. Fuzzy Sets Syst 86:289–298MATH

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

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

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

Chachi J, Taheri SM, Pazhand HR (2016) Suspended load estimation using L1-fuzzy regression, L2-fuzzy regression and MARS-fuzzy regression models. Hydrol Sci J 61:1489–1502

Chan KY, Lam HK, Dillon TS, Ling SH (2014) A stepwise-based fuzzy regression procedure for developing customer preference models in new product development. IEEE Trans Fuzzy Syst 23:1728–1745

Chan KY, Lam H, Yiu CKF, Dillon TS (2017) A flexible fuzzy regression method for addressing nonlinear uncertainty on aesthetic quality assessments. IEEE Trans Syst Man Cybern Syst 47:2363–2377

Chaudhuri A, De K (2009) Time series forecasting using hybrid neuro-fuzzy regression model. In: International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing, pp 369–381

Chen L, Nien S (2020) Mathematical programming approach to formulate intuitionistic fuzzy regression model based on least absolute deviations. Fuzzy Optim Decis Mak 19:191–210MathSciNetMATH

Chen JS, Ko CH, Pan S (2010) A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems. Inf Sci 180:697–711MathSciNetMATH

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

Cheng C, Lee ES (2001) Fuzzy regression with radial basis function network. Fuzzy Sets Syst 119:291–301MathSciNet

Cheng C, Low B, Chan P, Motwani J (2001) Improving the performance of neural networks in classification using fuzzy linear regression. Expert Syst Appl 20:201–206

Choi S Hoe, Jung H, Kim H (2019) Ridge fuzzy regression model. Int J Fuzzy Syst 21:2077–2090MathSciNet

Chukhrova N, Johannssen A (2019) Fuzzy regression analysis: systematic review and bibliography. Appl Soft Comput 84:105708. https://doi.org/10.1016/j.asoc.2019.105708 CrossRef

Ciavolino E, Calcagnì A (2016) A Generalized Maximum Entropy (GME) estimation approach to fuzzy regression model. Appl Soft Comput 38:51–63

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 51:267–286MathSciNetMATH

Danesh S, Farnoosh R, Razzaghnia T (2016) Fuzzy nonparametric regression based on an adaptive neuro-fuzzy inference system. Neurocomputing 173:1450–1460MATH

Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge, p 1MATH

De Hierro AFRL, Martínez-Moreno J, López R, Aguilar-Peña C (2016) Estimation of a fuzzy regression model using fuzzy distances. IEEE Trans Fuzzy Syst 24:344–359

Diamond P (1987) Least squares fitting of several fuzzy variables. Preprints of Second IFSA World Congress, Tokyo, pp 329–331

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

Diamond P, Kloeden P (1990) Metric spaces of fuzzy sets. Fuzzy Sets Syst 35:241–249MathSciNetMATH

Diamond P, Kloeden PE (1994) Metric spaces of fuzzy sets: theory and applications. World scientific, SingaporeMATH

Diamond P, Tanaka H (1998) Fuzzy regression analysis, fuzzy sets in decision analysis, operations research and statistics. Kluwer Academic Publishers, Norwell, pp 349–387MATH

Dubois DJ (1980) Fuzzy sets and systems: theory and applications. Mathematics in science and engineering. Academic press, CambridgeMATH

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

D’Urso P, Massari R (2013) Weighted least squares and least median squares estimation for the fuzzy linear regression analysis. Metron 71:279–306MathSciNetMATH

D’Urso P, Massari R, Santoro A (2011) Robust fuzzy regression analysis. Inf Sci 181:4154–4174MathSciNetMATH

Ebadi MJ, Suleiman M, Ismail FB, Ahmadian A, Shahryari MR, Salahshour S (2013) A new distance measure for trapezoidal fuzzy numbers. Math Problem Eng 2013

Fazlollahtabar H, Gholizadeh H (2020) Fuzzy possibility regression integrated with fuzzy adaptive neural network for predicting and optimizing electrical discharge machining parameters. Comput Ind Eng 140:106–225

Ferraro MB (2017) On the generalization performance of a regression model with imprecise elements. Int J Uncertain Fuzziness Knowl Based Syst 25:723–740MathSciNetMATH

Fukushima M (1992) Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math Program 53:99–110MathSciNetMATH

Fullér R (1995) Neural fuzzy systems. Citeseer, Princeton

Gong Y, Yang S, Ma H, Ge M (2018) Fuzzy regression model based on incentre distance and application to employee performance evaluation. Int J Fuzzy Syst 20:2632–2639

Hale JK (1969) Ordinary differential equations. Wiley, New YorkMATH

Hassanpour H, Maleki HR, Yaghoobi MA (2010) Fuzzy linear regression model with crisp coefficients: a goal programming approach. Iran J Fuzzy Syst 7:1–153MathSciNetMATH

He Y, Wang X, Huang JZ (2016) Fuzzy nonlinear regression analysis using a random weight network. Inf Sci 364:222–240MATH

He Y, Wei C, 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

Hee YJ, Seung CH (2013) Fuzzy least squares estimation with new fuzzy operations. In: Kruse R, Berthold M, Moewes C, Gil M, Grzegorzewski P, Hryniewicz O (eds) Synergies of soft computing and statistics for intelligent data analysis. Springer, Berlin, pp 193–202

Hesamian G, Akbari MG (2017) Semi-parametric partially logistic regression model with exact inputs and intuitionistic fuzzy outputs. Appl Soft Comput 58:517–526

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

Hosseinzadeh E, Hassanpour H, Arefi M (2015) A weighted goal programming approach to fuzzy linear regression with crisp inputs and type-2 fuzzy outputs. Soft comput 19:1143–1151MATH

Huang L, Zhang B, Huang Q (1989) Robust interval regression analysis using neural networks. Fuzzy Sets Syst 97:337–347

Ishibuchi H, Nii M (2001) Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. Fuzzy Sets Syst 119:273–290MathSciNetMATH

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

Ishibuchi H, Tanaka H, Okada H (1993) An architecture of neural networks with interval weights and its application to fuzzy regression analysis. Fuzzy Sets Syst 57:27–39MathSciNetMATH

Jeng J, Chuang C, Su S (2003) Support vector interval regression networks for interval regression analysis. Fuzzy Sets Syst 138:283–300MathSciNetMATH

Jung HY, Yoon JH, Choi SH (2015) Fuzzy linear regression using rank transform method. Fuzzy Sets Syst 274:97–108MathSciNetMATH

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317MathSciNetMATH

Kao C, Chyu CL (2003) Least-squares estimates in fuzzy regression analysis. Eur J Oper Res 148:426–435MathSciNetMATH

Khashei M, Hejazi SR, Bijari M (2008) A new hybrid artificial neural networks and fuzzy regression model for time series forecasting. Fuzzy Sets Syst 159:769–786MathSciNetMATH

Li J, Zeng W, Xie J, Yin Q (2016) A new fuzzy regression model based on least absolute deviation. Eng Appl Artif Intell 52:54–64

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

Lu J, Wang R (2009) An enhanced fuzzy linear regression model with more flexible spreads. Fuzzy Sets Syst 160:2505–2523MathSciNetMATH

Mendel JM (2014) On a novel way of processing data that uses fuzzy sets for later use in rule-based regression and pattern classification. Int J Fuzzy Logic Intell Syst 14:1–7

Miller RK, Miche AN (1982) Ordinary differential equations. Academic Press, New York

Mosleh M, Otadi M, Abbasbandy S (2010) Evaluation of fuzzy regression models by fuzzy neural network. J Comput Appl Math 234:825–834MathSciNetMATH

Mosleh M, Otadi M, Abbasbandy S (2011) Fuzzy polynomial regression with fuzzy neural networks. Appl Math Model 35:5400–5412MathSciNetMATH

Mosleh M, Allahviranloo T, Otadi M (2012) Evaluation of fully fuzzy regression models by fuzzy neural network. Neural Comput Appl 21:105–112

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

Nazemi AR (2018) A capable neural network framework for solving degenerate quadratic optimization problems with an application in image fusion. Neural Process Lett 47:167–192

Nazemi AR (2019) A new collaborate neuro-dynamic framework for solving convex second order cone programming problems with an application in multi-fingered robotic hands. Appl Intell 49:3512–3523

Neter J, Kutner MH, Nachtsheim CJ, Wasserman W (1969) Applied linear statistical models. Irwin, Chicago, p 4

Nikseresht A, Nazemi AR (2019) A novel neural network for solving semidefinite programming problems with some applications. J Comput Appl Math 350:309–323MathSciNetMATH

Otadi M (2014) Fully fuzzy polynomial regression with fuzzy neural networks. Neurocomputing 142:486–493

Pappis CP, Karacapilidis NI (1993) A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst 56:171–174MathSciNetMATH

Pehlivan NY, Apaydın A (2016) Fuzzy radial basis function network for fuzzy regression with fuzzy input and fuzzy output. Complex Intell Syst 2:61–73

Poleshchuk O, Komarov E (2010) Hybrid fuzzy least-squares regression model for qualitative characteristics. In: Huynh VN, Nakamori Y, Lawry J, Inuiguchi M (eds) Integrated uncertainty management and applications. Springer, Berlin, pp 187–196

Quarteroni A, Sacco R, Saleri F (2010) Numerical mathematics, vol 37. Springer, BerlinMATH

Rabiei MR, Arghami NR, Taheri SM, Gildeh BS (2014) Least-squares approach to regression modeling in full interval-valued fuzzy environment. Soft Comput 18:2043–2059MATH

Rabiei MR, Taheri SM, Arghami N (2015) A linear-programming approach to interval-valued fuzzy regression analysis. Int J Intell Technol Appl Stat (IJITAS) 8:171–203

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

Ramli AA, Watada J, Pedrycz W (2015) Information granules problem: an efficient solution of real-time fuzzy regression analysis. In: Pedrycz W, Chen SM (eds) Information granularity, big data, and computational intelligence. Sprinegr, Cham, pp 39–61

Rodriguez-Fdez I, Mucientes M, Bugarín A (2016) FRULER: Fuzzy rule learning through evolution for regression. Inf Sci 354:1–18

Roh S, Ahn T, Pedrycz W (2012) Fuzzy linear regression based on polynomial neural networks. Expert Syst Appl 39:8909–8928

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

Shen S, Mei C, Cui J (2010) A fuzzy varying coefficient model and its estimation. Comput Math Appl 60:1696–1705MathSciNetMATH

Somaye Y, Mahmood O, Niloofar I (2017) A new fuzzy regression model based on interval-valued fuzzy neural network and its applications to management. Beni-Suef Univ J Basic Appl Sci 6:2314–8535

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

Taheri SM, Salmani F, Abadi A, Majd HA (2016) A transition model for fuzzy correlated longitudinal responses. J Intell Fuzzy Syst 30:1265–1273MATH

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

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

Wang T, Shi P, Wang G (2020) Solving fuzzy regression equation and its approximation for random fuzzy variable and their application. Soft Comput 24:919–933

Xu R (1991) A linear regression model in fuzzy environment. Adv Model Simul 27:31–40MATH

Zadeh LA (1965) Information and control. Fuzzy Sets 8:338–353

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

Zhang Z, Lai Z, Xu Y, Shao L, Wu J, Xie GS (2017a) Discriminative elastic-net regularized linear regression. IEEE Trans Image Process 19:1466–1481MathSciNetMATH

Zhang T, Deng Z, Choi K, Liu J, Wang S (2017b) Robust extreme learning fuzzy systems using ridge regression for small and noisy datasets. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp. 1–7

Zhou J, Zhang H, Gu YP, Athanasios A (2018) Affordable levels of house prices using fuzzy linear regression analysis: the case of Shanghai. Soft Comput 22:5407–5418

Zimmermann HJ (2011) Fuzzy set theory and its applications. Springer, Berlin

Zolfaghari ZS, Mohebbi M, Najariyan M (2014) Application of fuzzy linear regression method for sensory evaluation of fried donut. Appl Soft Comput 22:417–423

Zuo H, Zhang G, Pedrycz W, Behbood V, Lu J (2016) Fuzzy regression transfer learning in Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 25:1795–1807

Zuo H, Zhang G, Pedrycz W, Behbood V, Lu J (2017) Granular fuzzy regression domain adaptation in Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 26:847–858

Titel: A parametric recurrent neural network scheme for solving a class of fuzzy regression models with some real-world applications
verfasst von: Delara Karbasi
Alireza Nazemi
Mohammadreza Rabiei
Publikationsdatum: 06.06.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 15/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-05008-1

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 15/2020

Solving an integrated cell formation and group layout problem using a simulated annealing enhanced by linear programming

The explicit solution of fuzzy singular differential equations using fuzzy Drazin inverse matrix

A new algorithmic decision for categorical syllogisms via Carroll’s diagrams

A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method

State theory on bounded hyper EQ-algebras

Dependency-aware software release planning through mining user preferences