It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers

Let suppose that

the closure of

Then the function

Properties (1)–(4) imply that for each

Also, the following statements hold:

the functions

Sometimes, the representation of fuzzy numbers with

In this study, we have used another type representation of a fuzzy number to avoid this type algebraic failure which is used in [

Furthermore, we know that shape similarity of the membership functions does not reflect the conception itself, but the context in which it is used. Whether a particular shape is suitable or not can be determined only in the context of a particular application. However, many applications are not overly sensitive to variations in the shape. In such cases, it is convenient to use a simple shape, such as the triangular shape of membership function.

For example, let us consider any triangular fuzzy number

If the function

Let

Let us suppose that

If we sum fuzzy number

The “

The second important matter is the topology on the set

The function

Let us denote the set of all sequences of fuzzy numbers by

Each subspace of

In [

By using the metric

Let

If the function

By Definition

Let

Let

Let the infinite matrix

Then the

The idea to construct a new sequence space of real or complex numbers using by matrix domain of a particular limitation method has been employed many authors; for example, you can see Altay et al. [

The sets

We consider only

Let us suppose that

In this section, we wish to introduce the

As we said above in (

Now, we may begin with the following theorem which is essential in the text.

The sequence spaces

We will only consider

Let

The sets

It was seen that in Theorem

Let

Other one of the best known matrix is

Let

Let

Let

The inclusions

To prove the validity of the inclusion

Let

Let us suppose that

Analogously to Talo and Başar, we can prove following proposition.

We know that each

Therefore, if

In this section, we state and prove the theorems determining the

The

Since the proof is similar for the rest of the spaces, we determine only

This is clear from Proposition

Define the sets

Consider

The

The proof of this theorem is similar to the proof of Theorem

For the first time, Lorentz introduced the concept of dual summability methods for the limitation which depends on a Stieltjes integral and passed to the discontinuous matrix methods by means of a suitable step function in [

Let us suppose that the set

Let us suppose that the sequences

It is clear here that the method

Let us assume the existence of the matrix product

Now we may give the following theorem concerning to the Zweier dual matrices.

Let

Suppose that

Let

Conversely, suppose that

Suppose that the elements of the infinite matrices

Let

Now, right here, we give the following propositions which are obtained from Lemma

Let

Let

Let

All praise is due to Allah who gave us to information and I wish, the idea of this paper will be guide to new research with related area.

The author declares that there is no conflict of interests regarding the publication of this paper.

The author would like to thank referee for his/her much encouragement, support, constructive criticism, careful reading and making a useful comment which improved the presentation and the readability of the paper.