In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

In this note we shall first strengthen Gage’s inequality as a more “isoperimetric-type” inequality. And then, we will use Minkowski’s support function to restate Gage’s inequality as an integral inequality which can be thought of as an analytic version of Gage’s inequality. Mathematics Subject Classification : 52A38, 52A40

This paper presents a novel method for combining multiple compensatory neural fuzzy networks (CNFN) using fuzzy integral. The fusion of multiple classifiers can overcome the limitations of a single classifier since the classifiers complement each other. A fuzzy integral is a better combination scheme than majority voting method that uses the subjectively defined relevance of classifiers. A comb...

The systems represented by the Choquet or the multi-linear fuzzy integral with respect to fuzzy measure is equivalently decomposable into hierarchically sub-systems through the use of Inclusion-Exclusion Covering (IEC) (Theorem 4.1,4.2) . Hence, IEC is one of very useful concepts/indexes for structural analysis of the fuzzy integral systems (short for: the systems represented by the Choquet or ...

In this paper, the cooperative games with fuzzy coalitions were discussed. Several integral representations which described the fuzzy character function of the cooperative game were given, and the important solution –-the Shapley function was also investigated. For the cooperative game where the rate of participation of every player in a coalition is allowed to range within interval [0,1], the ...

This paper describes the stepper motor position control implemented using a novel nonsingleton type-1 fuzzy logic system to update the gains of the professional proportional-integral-derivative controller running on ATMEGA 2560 microcontroller. In this work, three controllers are compared: a) the professional proportional-integral-derivative controller, b) the type-1 singleton fuzzy logic syste...

In this paper we define the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure. We show that the monotone convergence theorem and Fatou’s lemma are still true in this new setting. We study some of the properties of this integral, and show that it coincides with another fuzzy integral defmed in the literature. Our main result is a convergence theorem, that is in a...

In this paper the position control of a linear induction motor using adaptive fuzzy backstepping design with integral action is proposed. First, the indirect field oriented control for LIM is derived. Then, an integral backstepping design for indirect field oriented control of LIM is proposed to compensate the uncertainties which occur in the control. Finally, the fuzzy integral-backstepping co...