Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

A class of fuzzy neural networks (FNNs) with time-varying delays and impulses is investigated.With removing some restrictions on the amplification functions, a new differential inequality is established, which improves previouse criteria. Applying this differential inequality, a series of new and useful criteria are obtained to ensure the existence of global robust attracting and invariant sets...

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

The following is the classical Hermite-Hadamard inequality [4, 5]: f ( a+ b 2 ) ≤ 1 b− a (S) ∫ b a f(x)dμ ≤ f(a) + f(b) 2 . which provides estimates of the mean value of a convex function f on [a, b] where μ is the Lebesgue measure on R. This inequality in general, is not valid in the fuzzy context. In this paper, we find necessary and sufficient conditions of Hermite-Hadamard type inequality f...

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...

This paper proposes a new fuzzy adaptive exponential synchronization controller for uncertain time-delayed chaotic systems based on Takagi-Sugeno T-S fuzzy model. This synchronization controller is designed based on Lyapunov-Krasovskii stability theory, linear matrix inequality LMI , and Jesen’s inequality. An analytic expression of the controller with its adaptive laws of parameters is shown. ...

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

according to the ahlowalia hypothesis (1995), the growth of total factor productivity (tfp) beside infrastructure investments of government lead to income inequality decrease in rural areas of countries. the main objective of this study is to investigate the effects of public investments such as agricultural r&e, road, education and irrigation on income inequality in rural areas of iran. in...

This paper presents a new controller for speed control problem of the BLDC motors. The nonlinear model of the motor is approximated by implementation of fuzzy rules. The uncertainties are considered in the fuzzy system. Using this model and linear matrix inequality (LMI) optimization, a robust controller for purpose of speed control of the motor has been designed and applied to it. The effectiv...