A soft, rough set model is a distinctive mathematical model that can be used to relate a variety of real-life data. In the present work, we introduce new concepts of rough set based on soft pre-lower and soft pre-upper approximation space. These concepts are soft pre-rough equality, soft pre-rough inclusion, soft pre-rough belonging, soft pre-definability, soft pre-internal lower, and soft pre-external lower. We study the properties of these concepts. Finally, we use the soft pre-rough approximation to illustrate the importance of our method in decision-making for Chikungunya medical illnesses. In reality, the impact factors of Chikungunya's medical infection were determined. Moreover, we develop two new algorithms to address Chikungunya virus issues. Our proposed approach is sensible and effective.

The chikungunya virus is transmitted to humans by the bite of an infected mosquito. Fever and joint discomfort are the most typical symptoms of infection. Headache, muscle soreness, joint swelling, and rash are some of the other symptoms. The chikungunya virus was first discovered in the Americas in late 2013 on the Caribbean islands. The number of research articles published has exploded at a quick pace, particularly in mathematics. Several proposals were given for solving real-world problems with mathematical methodologies and relevant formulas to assist decision-makers in making the best decisions possible. To deal with challenges that are uncertain ([

To reduce the uncertainty and vagueness of knowledge, Molodtsov [

In our everyday lives, we are often constantly faced with challenges that necessarily require rational decision-making. Yet, we get uncertain about the correct answer in several of these situations. We must consider different criteria related to the solution in order to arrive at the best possible solution to these problems. For this, in our paper we can use the best mathematical tool namely soft, rough set theory in decision making. The classical soft sets were also applied to fuzzy soft sets by the same authors [

In this paper, we used this approximation to define many new concepts based on it, namely soft pre-rough belonging, soft pre-rough inclusion, soft pre-rough definability, soft pre-rough equality, and we studied the properties of these concepts. The present approximations are significant not just because they reduce or eliminate border areas. Finally, we will introduce an application in decision making of these concepts. At the end of the paper, we will present an algorithm that can be used to decide on an information system to show the importance of this approximation.

Here's how the document goes: Originality starts from

We offer some fundamental concepts and outcomes that are utilized in the paper:

We refer to _{s}

Clearly, if

The principal purpose of the following outcomes is to present and superimpose the fundamental features of soft pre-rough approximations

(i)

(ii)

(iii) I

(iv) If

(v)

(vi)

(vii)

(viii)

In this section, we presented the definitions of definability of sets by using soft pre-rough approximation, namely, soft pre-internal upper, soft pre-external lower of a set

The definition that follows introduces new concepts of definability for a subset

Soft pre-internally definable if and only if

Soft pre-externally definable if and only if

Soft pre-roughly undefinable if and only if

Soft pre-exact (briefly Soft pre-exact) set if and only if

Soft pre-internally definable (resp. Soft pre-externally definable and soft pre-exact).

Soft pre-internally definable set if and only if

Soft pre-externally definable set if and only if

Soft pre-external lower (briefly

Soft pre-external lower (briefly

Soft pre-exterior (briefly

Since

Since

Since

The following example shows the equality in (iii) of the above proposition.

Since

Since

Let

Let

In this section, we introduce new definitions on rough membership relation which indicates belonging to the elements of the set by using soft pre lower and soft pre upper approximations and we are studying some of their properties.

If

If

If

The next example clarifies the above remark. Also, this example shows the concepts of soft pre-lower belong and soft pre lower belong which we shall use in the following application.

If

If

If

Let

Let

Let

Let

Let

We will introduce in this section a new class of equality by using soft pre-lower and soft pre -upper approximations namely, soft pre lower equal, soft pre upper equal and approximations of any two sets and we study some of their properties.

The sets

The sets

The sets

If

If

Since

Since

Soft pre dense in

Soft pre co-dense in

Any set which contains soft pre dense is also soft pre dense set

Any subset of soft pre condense set is soft pre co-dense set

Let

Let

In this section, we present a new type of inclusion based on the soft pre rough approximation space called soft pre-upper inclusion, soft pre-lower inclusion, and soft pre-upper inclusion and we studied some of their results.

In the following example we show that the rough inclusion of sets does not imply to the inclusion of the ordinary sets.

If

If

If

Obvious.

Since

Similarly, as (

Similarly, as (

Since

Since

Since

Similarly (3).

It is obvious from (3), (4).

Since

Obvious.

This study concludes the method for dealing with chikungunya viral information. The algorithms (Algorithm 1, Algorithm 2) and frameworks (

Here we explore the problem of chikungunya, a disease that has been spread by Aedes mosquitoes that carry a virus that infects humans. CHIKV epidemics have occurred recently, linked to serious diseases. It generates a high temperature as well as significant joint discomfort. Muscle discomfort, headaches, and nausea are some of the other symptoms. The first signs and symptoms are similar to those of dengue fever. It typically does not endanger one's life. However, joint discomfort might linger for a long time. It might take months for you to fully heal. In most cases, the patient develops lifetime immunity to infection, making re-infection extremely unlikely. The illness has expanded throughout Africa and Asia in recent decades, particularly the subcontinent of India. Observe the table below, which contains information on 8-patients.

The following is a description of a set-valued information system in

Patients | Features ( |
Chikungunya | |||
---|---|---|---|---|---|

_{1} |
0 | 1 | 0 | 0 | 1 |

_{2} |
1 | 0 | 0 | 1 | 0 |

_{3} |
1 | 0 | 0 | 1 | 1 |

_{4} |
0 | 0 | 0 | 0 | 0 |

_{5} |
0 | 1 | 1 | 0 | 0 |

_{6} |
1 | 1 | 0 | 1 | 1 |

_{7} |
1 | 0 | 1 | 0 | 0 |

_{8} |
1 | 1 | 0 | 1 | 1 |

Let

In this section, the rules will be generated depending on the reduct. and core as in

Similarly, the strength of rule

Similarly, the strength of rule

Finally, we can find the strength of rules

Then, from the above calculations we find that the attributes _{3}}), …., then _{1}}), and superfluous are _{1,} _{2}.

Core attributes one removal with MATLAB program [

From this

Patients | Features ( |
Chikungunya | |
---|---|---|---|

_{1} |
0 | 0 | 1 |

_{2} |
0 | 1 | 1 |

_{3} |
0 | 1 | 0 |

_{4} |
0 | 0 | 0 |

_{5} |
1 | 0 | 0 |

Patients | Features ( |
Chikungunya | |
---|---|---|---|

_{1} |
0 | * | 1 |

_{2} |
0 | * | 1 |

_{3} |
0 | 1 | 0 |

_{4} |
* | 0 | 0 |

_{5} |
* | 0 | 0 |

Thus,

Patients | Features ( |
Chikungunya | |
---|---|---|---|

_{1} |
0 | * | 1 |

_{2} |
0 | 1 | 0 |

_{3} |
* | 0 | 0 |

In this article, we introduce the characteristics of the approach soft pre-rough set approximation and its decision making. We have introduced a new definition of this approach namely, soft pre-rough equality, soft pre-rough inclusion, soft pre-lower, soft pre-upper belong, soft pre-dense, soft pre-nowhere dense, soft pre-residual, soft pre-external lower and soft pre-internal upper and we also study some of their properties. We used our novel approach to identify the most important trait on the basis of its strength, which is an important method for analytical approach and decision making for any real-life problems. Also, we made a medical application to illustrate our method. This application can be used on any number of patients, any life problem and comment on the decision. Finally, the applicable technique is applied to a case study of a topological concept development strategy from the perspective of chikungunya virus in nature to validate the proposed method, as well as some comparison evaluations. We have explained our method with two algorithms and how to apply it using MATLAB. In reality, our suggestion is helpful in solving any future real-life problems. In the future, we shall extend the proposed methods to a variety of other concepts, such as the fuzzy set and fuzzy rough set.

The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work under the General Research Funding Program Grant Code (NU/-/SERC/10/603).