The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real an...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

In this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varyingdelays which are represented by the Takagi-Sugeno (T-S) fuzzy models is considered. A novel Linear Matrix Inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural...

This article deals with the robust stability analysis and passivity of uncertain discrete-time TakagiSugeno (T-S) fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help o...

A novel adaptive control strategy is proposed herein to increase the efficiency of adaptive control by combining Takagi–Sugeno (T–S) fuzzy modeling and the Ge–Yao–Chen (GYC) partial region stability theory. This approach provides two major contributions: (1) increased synchronization efficiency, especially for parameters tracing and (2) a simpler controller design. Two simulated cases are prese...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

The relevance of bifurcation analysis in Takagi–Sugeno (T–S) fuzzy systems is emphasized mainly through examples. It is demonstrated that even the most simple cases can show a great variety of behaviors. To understand the richness of asymptotic dynamics, one can find in T–S systems, a methodology is proposed by invoking bifurcation theory. Several local and global bifurcations (some of them, de...

In the paper aggregations of fuzzy relations using functions of n variables are considered. After recalling properties of fuzzy relations, aggregation functions which preserve: reflexivity, irreflexivity, T -asymmetry, T -antisymmetry, symmetry, S-connectedness, T -transitivity, negative Stransitivity, T -S-semitransitivity and T -S-Ferrers property of fuzzy relations, where T is a t-norm and S...

This paper proposes a Time Delay nonlinear dynamic model of HIV-1 (Human Immunodeficiency Virus type 1), introducing the drug consumption efficiencies as the controlling input for the model. The paper also represents the fuzzy T-S representation and the corresponding Fuzzy T-S controller. The controller parameters are tuned using LMIs (Linear Matrix Inequalities). The main focus is on the stabi...