An Adaptive Fuzzy Inference System Model to Analyze Fuzzy Regression with Quadratic Programming and Fuzzy Weights Incorporating Uncertainty in the Observed Data

Abstract

To address the compounded uncertainty in the observed output data, we introduce a new method of fuzzy regression modeling which is based on quadratic programming and fuzzy weights, so that the objective function represents the quadratic error for all of the central tendencies and the spreads. Also, the fuzzy weights are optimized for the fuzzy regression model estimation with crisp input and fuzzy output based on the adaptive fuzzy networks, considering symmetrical triangular fuzzy output. This paper aims to use the proposed method for the prediction of the output value in empirical applications where the observed value is a range or mean of several values, rather than a real fixed number. Two numerical examples were employed to demonstrate the efficiency of the method and compare the results of the proposed method with the previous ones such as linear programming (LP), quadratic programming (QP), as well as combination of linear programming and fuzzy weights (FWLP). The results show that the proposed method provides better prediction accuracy than other methods in surface roughness prediction of the grinding process.

Keywords

• uncertainty
• fuzzy regression
• linear programming
• quadratic programming
• adaptive fuzzy neural networks
• surface roughness
• grinding