In the last decades, more than a hundred families of fuzzy implication functions have been proposed. These are generated by adequately combining other logical connectives or univariate functions. However, no attention has given to final expression function, crucial feature for any application. this paper, polynomial implications introduced as those whose is two variables. Polynomials present ad...

This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result o...

One of the interesting, important and attractive problems in applied mathematics is how to best approximate a function in a given space. In this paper, the problem of best approximation is considered for fuzzy functions, by optimization to obtain a fuzzy polynomial.

— Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computerimplementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control. In some cases, fuzzy methodology is applied e...

In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.

Stability analysis of fuzzy control systems using polynomial methods is proposed. First, a new approach is introduced to search for poles of a T-S fuzzy system in any mixed weighting case. Next, through the technique of the pole placement, a controller can be designed to achieve the desired response. Then, using the following methods, such as the Kharitonov polynomials, Edge Theorem, Routh stab...

In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernstein polynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve t...

Whether a rule-based interval type-2 fuzzy system has the ability to approximate any continuous multivariate function arbitrarily well is a fundamentally important question for fuzzy control and modeling. The only approximation results available are the preliminary ones that we previously obtained. They state that two general classes of the interval T2 fuzzy systems, one for the Mamdani type an...