Tseng's forward-backward-forward splitting method for finding zeros of the sum Lipschitz continuous monotone and maximal operators is known to converge weakly in infinite dimensional Hilbert spaces. The inertial viscosity approximation techniques are widely used accelerate iterative algorithms obtain strong convergence, respectively. In this paper, we propose two fast, strongly convergent modif...

The matrix model with mass term has a nontrivially classical solution which is known to represent a noncommutative fuzzy sphere. The fuzzy sphere has a lower energy then that of the trivial solution. In this letter we investigate the quantum correction of the energy of the fuzzy sphere by using the Gaussian variational technique, in contrast to the other studying in which only the small fluctua...

We propose a novel variational approach to automatically soft-segment medical images into a fixed number of classes. Our method combines fuzzy classification and active contours in a single variational framework. This approach allows the use of tools from both deformable geometry and clustering in a well-defined setting and provides a useful, unsupervised segmentation technique. The model was t...

We introduce and study a new system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H ·, · -monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence...

In this note we introduce a variational problem with respect to an integrable fuzzy set f . The energy functional is maximized over a deleted σ -algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f . Finally an special case is considered where the variational problem can be transformed into a one dimensional se...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...

In this paper, we introduce and study a system of mixed variational-like inclusions and a system of proximal operator equations in Banach spaces which contains variational inequalities, variational inclusions, resolvent equations, system of variational inequalities and system of variational inclusions in the literature as special cases. It is established that the system of mixed variational-lik...

In this contribution, a fuzzy-set-based information retrieval model is considered. First, we show that the retrieval mechanism of such a retrieval model can be defined in terms of graded inclusion. This approach derives from the notion of division of fuzzy relations in the framework of Database Management Systems. Then, we point out different lines of extension of the graded inclusion aimed at ...