Fuzzy linear regression based on Polynomial Neural Networks

Authors:
Seok-Beom Roh;Tae-Chon Ahn;Witold Pedrycz
Affiliations:
School of Electronic and Control Engineering, Wonkwang University, Iksan, Chon-Buk 570-749, Republic of Korea;School of Electronic and Control Engineering, Wonkwang University, Iksan, Chon-Buk 570-749, Republic of Korea;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G7 and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Venue:
Expert Systems with Applications: An International Journal
Year:
2012

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Abstract

In this study, we introduce an estimation approach to determine the parameters of the fuzzy linear regression model. The analytical solution to estimate the values of the parameters has been studied. The issue of negative spreads of fuzzy linear regression makes the problem to be NP complete. To deal with this problem, an iterative refinement of the model parameters based on the gradient decent optimization has been introduced. In the proposed approach, we use a hierarchical structure which is composed of dynamically accumulated simple nodes based on Polynomial Neural Networks the structure of which is very flexible. In this study, we proposed a new methodology of fuzzy linear regression based on the design method of Polynomial Neural Networks. Polynomial Neural Networks divide the complicated analytical approach to estimate the parameters of fuzzy linear regression into several simple analytic approaches. The fuzzy linear regression is implemented by Polynomial Neural Networks with fuzzy numbers which are formed by exploiting clustering and Particle Swarm Optimization. It is shown that the design strategy produces a model exhibiting sound performance.