Fuzzy Random Regression to Improve Coefficient Determination in Fuzzy Random Environment

Determining the coefficient value is important to measure relationship in algebraic expression and to build a mathematical model though it is complex and troublesome. Additionally, providing precise value for the coefficient is difficult when it deals with fuzzy information and the existence of random information increase the complexity of deciding the coefficient. Hence, this paper proposes a fuzzy random regression method to estimate the coefficient values for which statistical data contains simultaneous fuzzy random information. A numerical example illustrates the proposed solution approach whereby coefficient values are successfully deduced from the statistical data and the fuzziness and randomness were treated based on the property of fuzzy random regression. The implementation of the fuzzy random regression method shows the significant capabilities to estimate the coefficient value to further improve the model setting of production planning problem which retain simultaneous uncertainties.

[1]  Norbert Meyer,et al.  Euro-Par 2006 Workshops: Parallel Processing , 2007, Lecture Notes in Computer Science.

[2]  J. Watada.  Building models based on environment with hybrid uncertainty , 2011, 2011 Fourth International Conference on Modeling, Simulation and Applied Optimization.

[3]  Witold Pedrycz,et al.  Building Confidence-Interval-Based Fuzzy Random Regression Models , 2009, IEEE Transactions on Fuzzy Systems.

[4]  Miin-Shen Yang,et al.  On cluster-wise fuzzy regression analysis , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Ana Colubi,et al.  Estimation of a simple linear regression model for fuzzy random variables , 2009, Fuzzy Sets Syst..

[6]  Elizabeth A. Peck,et al.  Introduction to Linear Regression Analysis , 2001 .

[7]  Ian T. Foster,et al.  Grid information services for distributed resource sharing , 2001, Proceedings 10th IEEE International Symposium on High Performance Distributed Computing.

[8]  Thomas Steinke,et al.  ZIB Structure Prediction Pipeline: Composing a Complex Biological Workflow Through Web Services , 2006, Euro-Par.

[9]  Ian Foster,et al.  The Grid 2 - Blueprint for a New Computing Infrastructure, Second Edition , 1998, The Grid 2, 2nd Edition.

[10]  George Emanuel,et al.  Definitions and Theorems , 1986 .

[11]  J. Tenenbaum,et al.  Predicting the future as Bayesian inference: people combine prior knowledge with observations when estimating duration and extent. , 2011, Journal of experimental psychology. General.

[12]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[13]  Wolfgang Näther.  Regression with fuzzy random data , 2006, Comput. Stat. Data Anal..

[14]  Steven Tuecke,et al.  The Physiology of the Grid An Open Grid Services Architecture for Distributed Systems Integration , 2002 .

[15]  M S Waterman,et al.  Identification of common molecular subsequences. , 1981, Journal of molecular biology.

[16]  Ian T. Foster,et al.  Grid Services for Distributed System Integration , 2002, Computer.

[17]  Nureize Arbaiy,et al.  Multi-level multi-objective decision problem through fuzzy random regression based objective function , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).