Takagi–Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzz...

In this paper, we introduce a new soft computing technique that dwells on the ideas of combining fuzzy rules in a fuzzy system with polynomial neural networks (PNN). The PNN is a flexible neural architecture whose structure is developed through the modeling process. Unfortunately, the PNN has a fatal drawback in that it cannot be constructed for nonlinear systems with only a small amount of inp...

In this paper, we propose a polynomial fuzzy observer-controller for nonlinear systems where the design is achieved through the stability analysis of polynomial-fuzzymodel-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback con...

We examine the properties of function approximation using polynomial rules in a fuzzy system. We show that this kind of fuzzy function approximation is equivalent to Lagrange polynomial interpolation between turning points when normalized fuzzy function memberships are used. The fuzzy inference procedure combines two polynomials of degree n and m in x into one single polynomial of at most degre...

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

In this paper, the stability of polynomial fuzzy-model-based (PFMB) observercontrol system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy mode...

In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To sho...

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function membersh...

We present a novel approach to fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which is a tight integration of fuzzy disjunctive logic programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly coupled disjunctive dl-programs by fuzzy vagueness in both the description logic...