The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...

The correlation between the performance of attributes and the overallsatisfaction such as they are perceived by the customers is often used tocalculate the importance of attributes in the crisp case. Recently, the methodwas extended, based on the standard Zadeh extension principle, to the fuzzycase, taking into account the specificity of the human thinking. Thedifficulties of calculation are im...

Abstract For the linear Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate error constant under maximum norm by using finite-element method (FEM). In solving optimization problem corresponding constant, in constraint condition is most difficult part process. To handle this difficulty, novel proposed combining orthogonality of space decompos...

We revisit a classical scenario in communication theory: a source is generating a waveform which we sample at regular intervals; we wish to transform the signal in such a way as to minimize distortion in its reconstruction, despite noise. The transformation must be online (also called causal), in order to enable real-time signaling. The noise model we consider is adversarial `1-bounded; this is...

We investigate, by direct numerical simulations, the dynamics of damped and forced nonlinear Schr\"odinger (NLS) equation in presence a time periodic forcing for certain parametric regimes. It is thus revealed, that wave-number plane-wave initial condition dictates number emerged Peregrine type rogue waves at early stages modulation instability. The formation these events gives rise to same tra...

Abstract. We consider here the linear least squares problem miny∈Rn ‖Ay− b‖2, where b ∈ Rm and A ∈ Rm×n is a matrix of full column rank n, and we denote x its solution. We assume that both A and b can be perturbed and that these perturbations are measured using the Frobenius or the spectral norm for A and the Euclidean norm for b. In this paper, we are concerned with the condition number of a l...

We give an upper bound for the L condition number of the triangular Bernstein basis for polynomials of total degree at most n in s variables. The upper bound grows like (s + 1) when n tends to infinity. Moreover the upper bound is independent of s for s ≥ n− 1.

Let 1 < p < ∞ and A = (an,k)n,k 1 be a non-negative matrix. Denote by ‖A‖w,p,F , the infimum of those U satisfying the following inequality: ‖Ax‖w,p,F U ‖x‖w,p,I , where x 0 and x ∈ lp(w,I) and also w = (wn)n=1 is a decreasing, non-negative sequence of real numbers. The purpose of this paper is to give a lower bound for ‖A‖w,p,F , where A is a lower triangular matrix. In particular, we apply ou...