The aim of this paper is to introduce an abstract framework of certain

approximation processes using a cosine operator functions concept.

The mean-value first-order saddlepoint

approximation (MVFOSA) [4] is an alternative to FOSA.

Different from one-piecewise linear

approximation used in [6], a three-piecewise linear

approximation is presented to compute the initial seed in this paper.

The remaining part of this paper is organized as follows: we recall the basic notions of rough set, standard neutrosophic set and rough standard neutrosophic set on the crisp

approximation space, respectively, in Sections 2 and 3.

Figure 1 depicts a band-limited signal and its finite sum

approximation according to:

However, there are no contributions on the definitions of

approximation operators of general type-2 fuzzy sets in the Pawlak

approximation space and the generalized Pawlak

approximation space.

In similar cases it is applied or piecewise

approximation [1], or a spline

approximation [4, 5, 6, 7].

The following

approximation theorem for a sequence of positive linear operators acting from [L.

In the first step of developing the

approximation algorithm a set of neural networks were tested based on preliminary results given by [8].

The next

approximation takes the rectangle to a trapezoid, reflecting the realization that the circumference of the bell at the mouth is larger than at the crown.

The more classical examples of linear positive operators throughout

approximation process are the Bernstein polynomials, which are defined by Bernstein [3] as following:

In comparison with the standard finite element method, the characteristics of mesh-independent and wave-based

approximation effectively make the meshfree methods attractive alternative numerical techniques for modeling the waveguide problems.