Fuzzy prediction strategies for gene-environment networks – Fuzzy regression analysis for two-modal regulatory systems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 2, pp. 413-435.

Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks consist of two major groups of entities that are interacting by unknown relationships. The structure and dynamics of the hidden regulatory system have to be revealed from uncertain measurement data. In this paper, the concept of fuzzy target-environment networks is introduced and various fuzzy possibilistic regression models are presented. The relation between the targets and/or environmental entities of the regulatory network is given in terms of a fuzzy model. The vagueness of the regulatory system results from the (unknown) fuzzy coefficients. For an identification of the fuzzy coefficients’ shape, methods from fuzzy regression are adapted and made applicable to the bi-level situation of target-environment networks and uncertain data. Various shapes of fuzzy coefficients are considered and the control of outliers is discussed. A first numerical example is presented for purposes of illustration. The paper ends with a conclusion and an outlook to future studies.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2015044
Classification : 92-08, 92D10, 62J86
Mots clés : Fuzzy evolving networks, fuzzy target-environment networks, uncertainty, fuzzy theory, fuzzy regression analysis, possibilistic regression, forecasting
Kropat, Erik 1 ; Özmen, Ayşe 2 ; Weber, Gerhard-Wilhelm 2 ; Meyer-Nieberg, Silja 3 ; Defterli, Ozlem 4

1 Institute for Applied Computer Science, Universität der Bundeswehr München, 85577 Neubiberg, Germany.
2 Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey.
3 Institute for Theoretical Computer Science, Mathematics and Operations Research, Universität der Bundeswehr München, 85577 Neubiberg, Germany.
4 Faculty of Arts and Sciences, Department of Mathematics and Computer Science,Çankaya University, 06810 Ankara, Turkey.
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     title = {Fuzzy prediction strategies for gene-environment networks {\textendash} {Fuzzy} regression analysis for two-modal regulatory systems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Kropat, Erik; Özmen, Ayşe; Weber, Gerhard-Wilhelm; Meyer-Nieberg, Silja; Defterli, Ozlem. Fuzzy prediction strategies for gene-environment networks – Fuzzy regression analysis for two-modal regulatory systems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 2, pp. 413-435. doi : 10.1051/ro/2015044. http://www.numdam.org/articles/10.1051/ro/2015044/

C. Carleos, F. Rodriguez, H. Lamelas and J.A. Baro, Simulating complex traits influenced by genes with fuzzy-valued effects in pedigreed populations. Bioinform. 19 (2003) 144–148. | DOI

Y.-H.O. Chang and B.M. Ayyub, Fuzzy regression methods – a comparative assessment. Fuzzy Sets Syst. 119 (2001) 187–203. | DOI | MR

S. Charfeddine, K. Zbidi and F. Mora-Camino, Fuzzy Regression Analysis Using Trapezoidal Fuzzy Numbers. In Proc. of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology and the 11th Rencontres Francophones sur la Logique Floue et ses Applications, edited by E. Montseny, P. Sobrevilla. Barcelona, Spain (2005).

O. Defterli, A. Fügenschuh and G.-W. Weber, Modern tools for the time-discrete dynamics and optimization of gene-environment networks. Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 4768–4779. | DOI | MR | Zbl

E. Dere, A.L. Forgacs, T.R. Zacharewski and L.D. Burgoon, Genome-wide computational analysis of dioxin response element location and distribution in the human, mouse, and rat genomes. Chem. Res. Toxicol. 24 (2011) 494–504. | DOI

P. Diamond, Fuzzy least squares source. Inform. Sci. 46 (1988) 141–157. | DOI | MR | Zbl

J. Gebert, M. Lätsch, E.M.P. Quek and G.-W. Weber, Analyzing and optimizing genetic network structure via path-finding. J. Comput. Technol. 9 (2004) 3–12. | Zbl

T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning. Springer (2001). | MR | Zbl

H. Ishibuchi and M. Nii, Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. Fuzzy Sets Syst. 199 (2001) 273–290. | DOI | MR | Zbl

C. Kahraman, A. Beskese and F. Tunc Bozbura, Fuzzy Regression Approaches and Applications. In Fuzzy Applications in Industrial Engineering. Vol. 201 of Studies in Fuzziness and Soft Computing. Springer, Berlin, Heidelberg (2006), 589–615.

G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, New Jersey (1995). | MR | Zbl

E. Kropat, Fuzzy-Unabhängigkeitssysteme und Fuzzy-Matroide. Wissenschaftlicher Verlag Berlin, Berlin (2002).

E. Kropat, G.-W. Weber and B. Akteke-Öztürk, Eco-finance Networks Under Uncertainty. In Proc. of the International Conference on Engineering Optimization, EngOpt 2008, edited by J. Herskovits, A. Canelas, H. Cortes, M. Aroztegui. Rio de Janeiro, Brazil, 1-5 June 2008.

E. Kropat, G.-W. Weber and J.-J. Rückmann, Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization. Dyn. Contin. Discrete Impulsive Syst. Ser. B 17 (2010) 639–657. | MR | Zbl

E. Kropat, G.-W. Weber and S. Belen, Dynamical Gene-environment Networks Under Ellipsoidal Uncertainty - Set-theoretic Regression Analysis Based on Ellipsoidal OR. In Vol. 1 of Dynamics, Games and Science I. Springer Proc. Math., edited by M.M. Peixoto, A.A. Pinto, D.A. Rand. Springer-Verlag, Berlin, Heidelberg (2011) 545–571. | MR | Zbl

E. Kropat, G.-W. Weber and C.S. Pedamallu, Regulatory Networks Under Ellipsoidal Uncertainty - Data Analysis and Prediction by Optimization Theory and Dynamical Systems. In Data Mining: Foundations and Intelligent Paradigms, edited by D.E. Holmes, L.S. Jain. Vol. 2 of Statistical, Bayesian, Time Series and other Theoretical Aspects, ISRL 24. Springer-Verlag, Berlin (2012) 27–56. | MR | Zbl

E. Kropat, G.-W. Weber, S.Z. Alparslan-Gök and A. Özmen, Inverse Problems in Complex Multi-modal Regulatory Networks Based on Uncertain Clustered Data. In Modeling, Optimization, Dynamics and Bioeconomy, edited by A. Pinto and D. Zilberman. Springer (2014) 437–451. | MR

D.S. Malik and J.N. Mordeson, Fuzzy Discrete Structures. Physica-Verlag, Heidelberg (2000). | Zbl

S. Meyer–Nieberg and E. Kropat, Tracking Targets under Uncertainty: Natural Computing Approaches. In Proc. of the 47th Hawaii International Conference on Systems Sciences, January 6-9, 2014. Waikoloa, Big Island, Hawaii (2014) 1162–1171.

G. Peters, Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst. 63 (1994) 45–55. | DOI | MR

D.T. Redden and W.H. Woodall, Properties of certain fuzzy linear regression methods. Fuzzy Sets Syst. 64 (1994) 361–375. | DOI | MR | Zbl

M. Sakawa and H. Yano, Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets Syst. 47 (1992) 173–181. | DOI | Zbl

D.A. Savic and W. Pedrycz, Evaluation of fuzzy linear regression models. Fuzzy Sets Syst. 39 (1991) 51–63. | DOI | MR | Zbl

H. Tanaka and H. Ishibuchi, Possibilistic Regression Analysis Based on Linear Programming. In: Fuzzy Regression Analysis, edited by J. Kacprzyk, M. Fedrizzi. Physica-Verlag, Heidelberg (1992) 47–60. | MR

H. Tanaka, K. Uejima and K. Asai, Linear regression analysis with fuzzy model. IEEE Systems Trans. Systems Man Cybernet. 12 (1982) 903–907. | DOI | Zbl

H. Tanaka, I. Hayashi and J. Watada, Possibilistic linear regression analysis for fuzzy data. Eur. J. Oper. Res. 40 (1989) 389–396. | DOI | MR | Zbl

H. Tanaka, H. Ishibuchi and S.G. Hwang, Fuzzy model of the number of staff in local government by fuzzy regression analysis with similarity relations. J. Jpn Indust. Management Assoc. 41 (1990) 99–104.

M. Taştan, Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm. MSc thesis, Institute of Applied Mathematics, METU, Turkey (2005).

Ö. Uğur and G.-W. Weber, Optimization and dynamics of gene-environment networks with intervals, in the Special Issue at the occasion of the 5th Ballarat Workshop on Global and Non-Smooth Optimization: Theory, Methods and Applications, November 28–30, 2006. J. Ind. Manag. Optim. 3 (2007) 357–379. | MR | Zbl

G.-W. Weber, Charakterisierung struktureller Stabilität in der nichtlinearen Optimierung. In Aachener Beiträge zur Mathematik 5, edited by H.H. Bock, H.T. Jongen, and W. Plesken. Augustinus publishing house (now: Mainz publishing house), Aachen (1992). | Zbl

G.-W. Weber, Generalized semi-infinite optimization and related topics, edited by K.H. Hofmannn and R. Wille. In vol. 29 of Research and Exposition in Mathematics. Lemgo, Heldermann Publishing House (2003) | MR | Zbl

G.-W. Weber, S.Z. Alparslan-Gök and N. Dikmen, Environmental and life sciences: gene-environment networks – optimization, games and control – a survey on recent achievements. Invited paper. J. Organisational Transformation and Social Change 5 (2008) 197–233. | DOI

G.-W. Weber, P. Taylan, S.-Z. Alparslan-Gök, S. Özöğür and B. Akteke-Öztürk, Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation. TOP Oper. Res. J. SEIO (Spanish Statistics and Operations Research Society) 16 (2008) 284–318. | MR | Zbl

G.-W. Weber, A. Tezel, P. Taylan, A. Soyler and M. Çetin, Mathematical contributions to dynamics and optimization of gene-environment networks. In Special Issue: In Celebration of Prof. Dr. Hubertus Th. Jongen’s 60th Birthday, edited by D. Pallaschke, O. Stein. J. Optim. 57 (2008) 353–377. | MR | Zbl

G.-W. Weber, S.Z. Alparslan-Gök and B. Söyler, A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics. Environ. Model. Assess. 14 (2009) 267–288. | DOI

G.-W. Weber, E. Kropat, B. Akteke-Öztürk and Z.-K. Görgülü, A Survey on OR and Mathematical Methods Applied on Gene-Environment Networks. Special Issue on “Innovative Approaches for Decision Analysis in Energy, Health, and Life Sciences” at the occasion of EURO XXII 2007, Prague, Czech Republic, July 8–11 (2007). Central Eur. J. Oper. Res. 17 (2009) 315–341. | MR | Zbl

G.-W. Weber, S. Özögür-Akyüz and E. Kropat, A review on data mining and continuous optimization applications in computational biology and medicine. Embryo Today, Birth Defects Research C 87 (2009) 165–181. | DOI

G.-W. Weber, Ö. Uğur, P. Taylan and A. Tezel, On optimization, dynamics and uncertainty: A tutorial for gene-environment networks. In the Special Issue Networks in Computational Biology. Discrete Appl. Math. 157 (2009) 2494–2513. | DOI | MR | Zbl

G.-W. Weber, E. Kropat, A. Tezel and S. Belen, Optimization applied on regulatory and eco-finance networks – survey and new developments. Special Issue in memory of Professor Alexander Rubinov, edited by M. Fukushima. Pacific J. Optim. 6 (2010) 319–340. | MR | Zbl

G.-W. Weber, O. Defterli, S.Z. Alparslan-Gök and E. Kropat, Modeling, inference and optimization of regulatory networks based on time series data. Eur. J. Oper. Res. 211 1–14 (2011) | DOI | MR | Zbl

F.B. Yılmaz, H. Öktem and G.-W. Weber, Mathematical Modeling and Approximation of Gene Expression Patterns and Gene Networks. In Operations Research Proceedings, edited by F. Fleuren, D. den Hertog and P. Kort (2005) 280–287.

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