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The notion of intersectional soft subalgebras of a BE-algebra is introduced, and related properties are investigated. Characterization of an intersectional soft subalgebra is discussed. The problem of classifying intersectional soft subalgebras by their inclusive subalgebras will be solved.

In 1966, Imai and Iséki [

Various problems in system identification involve characteristics which are essentially nonprobabilistic in nature [

In this paper, we introduce the notion of int-soft subalgebras of a

Let

A relation “

A

A

Note that every self distributive

A mapping

A soft set theory is introduced by Molodtsov [

In what follows, let

A soft set

The function

In what follows, denote by

For any soft sets

Assume that

For a soft set

In what follows, we take

A soft set

Let

Let

Let

A soft set

The subalgebra

Assume that

Conversely, suppose that

Every int-soft subalgebra

Using (

For any int-soft subalgebra

Assume that a fixed element

Let

Taking

For any

(1) The soft set

(2) The soft set

For any

Note that

Let

For any

Let

Let

Let

If

If

Let

The following example shows that the soft union of int-soft subalgebras over

Let

Let

Straightforward.

The converse of Theorem

Let

Let

Since

Let

Let

We have the following question.

The following example shows that the answer to the question above is false.

Let

However, we have the following theorem.

Every subalgebra of a

Let

Note that if

Let

Let

Conversely, suppose that there is no

As a consequence of Theorem

Let

Let

Let

The following example shows that two int-soft subalgebras over

Let

Let

Straightforward.

Let

(1)

(2)

(3)

Corollary

(2) Using (1) and Remark

(3) Let

Let

Consider a class

Theorem

Let

Let

Let

Using the notion of int-soft sets, we have introduced the concept of int-soft subalgebras in

every soft image of an int-soft subalgebra is also an int-soft subalgebra;

the soft intersection of int-soft subalgebras is an int-soft subalgebra.

We have made a new int-soft subalgebra from the old one. Work is ongoing. Some important issues for future work are as follows:

to develop strategies for obtaining more valuable results,

to apply these notions and results for studying related notions in other (soft) algebraic structures,

to study the soft set application in ideal and filter theory of

The authors wish to thank the anonymous reviewer(s) for their valuable suggestions. This work (RPP-2012-021) was supported by the fund of Research Promotion Program, Gyeongsang National University, 2012.