web usage mining (wum) is the automatic discovering of hidden informationof user access pattern from the web log data. frequent pattern discovery is one ofthe main techniques in wum that can be used to implement recommender systems,forecast user`s navigational behaviour, and personalize web sites. many algorithmshave been suggested on obtaining frequent user navigation patterns. this paperprese...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

Abstract. Combining both kinds of fuzzy logic forms including fuzzy T-S model and adaptive fuzzy logic systems, this paper presents an observer-based ∞ H control scheme for a class of uncertain nonlinear timedelay systems. Firstly, the fuzzy T-S model is used to approximate the nonlinear systems, and an observer is designed to observe the system states, and the fuzzy control law of the fuzzy mo...

Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be fou...

This paper presents new relaxed stability conditions and LMI(linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno’s fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented ...

According to mathematical properties of continuous function, the universal approximation properties of fuzzy mapping in only one interval are analyzed, and some related theorems are proposed and proved. Then, the sufficient conditions of the general T-S fuzzy systems with universal approximation are derived from these theorems, which helps establish the new relationship between approximation er...

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T-S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) stru...

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion an...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

In recent years, there has been significant interest in the study of stability analysis and con‐ troller synthesis for Takagi-Sugeno(T-S) fuzzy systems, which has been used to approximate certain complex nonlinear systems [1]. Hence it is important to study their stability analysis and controller synthesis. A rich body of literature has appeared on the stability analysis and synthesis problems ...