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In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness. In this paper, we apply the concept of soft sets to

Most of the problems in engineering, medical science, economics, environments, and so forth, have various uncertainties. The problems in system identification involve characteristics which are essentially nonprobabilistic in nature. In response to this situation, Zadeh [

In this section, we recall some basic concepts that are necessary for subsequent discussion of

The notion of a

Let

A

If a

A nonempty subset

A pair

It is clear to see that a soft set is a parameterized family of subsets of the set

Let

The restricted intersection of a nonempty family soft sets

The extended intersection of a nonempty family soft sets

The restricted union of a nonempty family soft sets

The

The

The Cartesian product of the nonempty family soft sets

For a soft set

We refer the readers to the papers [

If

Let

Let

Consider the

Consider the

Let

if

if

Let

Let

Let

Let

Let

Suppose that

Let

Let

Let

Assume that

Let

Let

Let

Let

Let

If

The converse of above theorem is not true in general, and it can be seen in the following example.

Consider the

A soft

Let

Let

Let

Let

Let

Let

In this definition, if

Let

This is an improper

Consider the

We state the following propositions without their proofs.

Let

The soft function

If

Let

Let

Let

Let

We will prove second part. We show that

we show that

We now show that

Consider

We now introduce the concept of soft intersection soft

Let

Assume that

From now on, we will always assume that

Let

Let

Let

Let

Let

Let

Let

Let

Hence,

Let

Let

Straightforward.

Let

Let

Let

Let

Let

Since

Presently, science and technology are featured with complex processes and phenomena for which complete information is not always available. For such cases, mathematical models are developed to handle various types of systems containing elements of uncertainty. A large number of these models are based on an extension of the ordinary set theory, namely, soft sets. In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness, and many researchers have created some models to solve problems in decision making and medical diagnosis. We have applied the concept of soft set theory to

The authors are highly thankful to the referees for their valuable comments and suggestions.