Abstract
This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form y_{p}=a_{n}x_{p}^n+ cdots +a_{1}x_{p}+a_{0} where a_{j} is crisp number (for j=0,ldots ,n), which interpolates the fuzzy data (x_{j},y_{j}),(for,j=0,ldots ,n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.
Highlights
Artificial neural networks (ANNs) are mathematical or computational models based on biological neural networks
There have been rapid growth of ANNs which was utilized in various fields (Abbasbandy and Otadi 2006; Chen and Zhang 2009; Guo and Qin 2009; Jafarian and Jafari 2012; Jafarian et al 2015a, b; Jafarian and Measoomynia 2011, 2012; Song et al 2013; Wai and Lin 2013)
One of the vital roles of ANN is finding FIPs as it proposed in this research
Summary
Artificial neural networks (ANNs) are mathematical or computational models based on biological neural networks. Interpolation has been used extensively, because it is one of the noteworthy techniques of function approximation (Boffi and Gastaldi 2006; Mastylo 2010; Rajan and Chaudhuri 2001). Using Newton’s divided difference scheme, a new technique was established in Schroeder et al (1991) for polynomial interpolation. The problem related to multivariate interpolation has grabbed the attention of researchers world wide (Neidinger 2009; Olver 2006). In Olver (2006) they used a multivariate Vandermode matrix and its LU factorization, and Neidinger (2009) utilized the Newton-form interpolation. We recall that sparse grid interpolation is a further technique. In recent years this procedure is widely executed for the provision of an average approximation to a smooth function (Xiu and Hesthaven 2005). Utilizing the Lagrange interpolating polynomials, this approach
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
