This paper presents a sum of squares (SOS) approach to guaranteed cost control of polynomial discrete fuzzy systems. First, we present a polynomial discrete fuzzy model that is more general representation of the well-known discrete Takagi-Sugeno (T-S) fuzzy model. Secondly, we derive a design condition based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special...

This paper discusses a general approach to qualitative modeling based on fuzzy logic. The method of qualitative modeling is divided into two parts: fuzzy modeling and linguistic approximation. It proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, a...

Abstract— Studies on the effectiveness of fuzzy logic for nonlinear modeling are presented. Although successful applications of fuzzy logic in many diverse areas are reported in the literature, commonly the explicit description of the key features of fuzzy logic yielding these outcomes is not addressed. The present research addresses this issue, to understand the basic features of fuzzy logic i...

This paper is concerned with a design method for modeling Incremental Granular Model (IGM) based on Linguistic Model (LM) and Polynomial Regression (PR) from data set obtained by complex yacht hydrodynamics. For this purpose, we develop a systematic approach to generating automatic fuzzy rules based on Context-based Fuzzy C-Means (CFCM) clustering. This clustering algorithm builds information g...

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...

This paper deals with the problem of automatic rule generation for fuzzy systems design. The proposed approach is based on hybrid artificial bee colony (ABC) optimization and weighted least squares (LS) method and aims to find the structure and parameters of fuzzy systems simultaneously. More precisely, two ABC based fuzzy modeling strategies are presented and compared. The first strategy uses ...

Running average method and its modified version are two simple and fast methods for background modeling. In this paper, some weaknesses of running average method and standard background subtraction are mentioned. Then, a fuzzy approach for background modeling and background subtraction is proposed. For fuzzy background modeling, fuzzy running average is suggested. Background modeling and backgr...

The fuzzy logic concept provides a natural way of dealing with problems in which the source of imprecision is an absence of sharply defined criteria rather than the presence of random variables. The fuzzy approach considers cases where uncertainties play a role in the control mechanism of the concerned phenomena. Fuzzy modeling includes fuzzification, fuzzy analysis and defuzzification. In this...