We prove a more general version of the Grüss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-α derivative and integral. For the particular case when α = 1, one gets a delta-integral Grüss inequality on time scales; for α = 0 a nabla-integral Grüss inequality. If we further restrict ourselves by fixing the time scale to...

Given a real valued random variable Θ we consider Borel measures μ on B(R), which satisfy the inequality μ(B) ≥ Eμ(B−Θ) (B ∈ B(R)) (or the integral inequality μ(B) ≥ R∞ −∞ μ(B−h)γ(dh)). We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

The aim of this paper is to study monadic L-fuzzy quantifiers of the type 〈1〉 determined by fuzzy measures. These fuzzy quantifiers are defined using a novel notion of ⊗-fuzzy integral. Several semantic properties of these L-fuzzy quantifiers are studied. Keywords— fuzzy integral, fuzzy logic, fuzzy measure, fuzzy quantifier, generalized quantifier

Fuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions areapproved and an upper bound for them are determined. Finally an algorithmis drawn to show theorems better.

This paper presents improved stability results by introducing a new delay partitioning method based on the theory of geometric progression to deal with T-S fuzzy systems in the appearance of interval time-varying delays and nonlinear perturbations. A common ratio [Formula: see text] is applied to split the delay interval into multiple unequal subintervals. A modified Lyapunov-Krasovskii functio...

This study introduces the fuzzy Lyapunov function to the fuzzy PID control systems, modified fuzzy systems, with an optimized robust tracking performance. We propose a compound search strategy called conditional linear matrix inequality (CLMI) approach which was composed of the proposed improved random optimal algorithm (IROA) concatenated with the simplex method to solve the linear matrix ineq...

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction dif...