The theory of fuzzy sets is used in various Mathematical fields. Zadeh [1] 1965 developed the concept of fuzzy sets which is the basis of fuzzy Mathematics. Since then various researchers worked on the development of fuzzy set theory. Atanassov [2,3,4,5,6,7] has given idea about intuitionistic fuzzy sets. Im and Lee [8] studied about the determinant of square intuitionistic fuzzy matrices (IFMs...

This paper deals with control design and stability analysis for a class of nonlinear systems with system uncertainties as well as input constraint when using the T-S fuzzy model. As a result, it achieves an adaptive fuzzy controller, which consists of two components: one is corresponding with the regular state feedback controller based on the LMI approach in order to deal with the known part in...

In this paper, the nearest symmetric fuzzy solution for a symmetric L-L fuzzy linear system (S-L-FLS) is obtained by a new metric. To this end, the S-L-FLS is transformed to the non-linear programming problem (NLP). The solution of the obtained NLP is our favorite fuzzy number vector solution. Also, it is shown that if an S-L-FLS has unique fuzzy solution, then its solution is symmetric. Two co...

The concepts of ∈-soft sets and q-soft sets in AG-groupoids are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy interior ideals and soft interior ideals over an AG-groupoid S. Moreover, we study the relation-ships among (∈, ∈ ∨q)fuzzy interior ideals, ( ) , q ∈∈∨ -fuzzy interior ideals, (α; β)-fuzzy interior ideals and s...

Fuzzy inclusion dependencies ( , [0, FID s α 1]) α ∈ express subset-relationships between fuzzy databases and are thus important indicators for redundancies between fuzzy databases. In general, the discovery of FID s α will be beneficial in any effort to integrate unknown fuzzy databases. The problem of searching FID s α between two fuzzy relations is NP-hard. Therefore, we have mapped the FID ...

Since the T-S fuzzy system can approximate any nonlinear system with arbitrary accuracy, it is also expected to be a suitable approach to observe the states of a stochastic nonlinear system. Up to date, a few state estimators for stochastic T-S fuzzy systems have been proposed and applied to various fields without rigorous proof. In this paper, we first derive a sufficient condition based on th...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

This paper deals with the fuzzy based H∞ control problem for time-delay affine Takagi-Sugeno (T-S) fuzzy models. A class of nonlinear time-delay systems is approximated by a time-delay affine T-S fuzzy model in this paper. Based on LyapunovRazumikhin theorem and S-procedure, the stability and stabilization problems are solved by employing a Parallel Distributed Compensation (PDC) type H∞ fuzzy ...

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...

Abstract The output feedback stabilization for discrete nonlinear systems is studied based on T-S fuzzy model in this paper. Firstly, a concept of the efficient mutual non-neighboring rule group (EMNNRG) is presented. Secondly, by using the scheme of parallel distributed compensation (PDC) and the piecewise fuzzy Lyapunov function, the stability of the closed-loop discrete T-S fuzzy control sys...