Fuzzy system modeling using linear distance rules (Q1965294)

This paper is concerned with a multivariable (\(n\)-input) rule-based fuzzy model. The rules under discussion are of the form Rule-\(j\): \hskip 17mm if (\(x_1\) is \(A_{j1}\) and \(x_2\) is \(A_{j2}\) and\dots and \(x_n\) is \(A_{jn}\)) then \hskip 17mm \(y= a_{j0}+ a_{j1}(x_1- c_{j1})+ a_{j2}(x_2- c_{j2})+\cdots+ a_{jn}(x_n- c_{jn})\), where \(A_{ji}\), \(i= 1,2,\dots, n\), are the fuzzy sets in the input space and \(a_{ji}\), \(i= 0,2,\dots, n\) and \(c_{ji}\), \(i= 1,2,\dots, n\) are the parameters of the conclusion part of the rules. Moreover, \(c_{ji}\) are the centers of the Gaussian-like membership functions (fuzzy sets) defined in the space of the input variables. The rules in the above form are referred to as linear distance rules. The neural network realization of this inference model is introduced along with a learning scheme. In the sequel, a way of reducing the number of input variables is discussed.