# Soft Set Based Summarization Model

(Applications of Approximate Learning)

Soft set basically deal with uncertain data which is not precisely classified into one domain of required characterization. Note one domain may be approximate while in another domain of knowledge the same problem may be precise. This can be understood as political parties example, in one domain a political party voting choises are quite vague while in another city the voting decisions are precise and well established.

In this short article I am presenting Soft Set based Summarization model. This is quite an uncertainty handling problem, given a sentence selection problem can be uncertain from following point of views:

1. The choice of sentences itself includes uncertainty handling, which is more that the word sense disambuiguation task covered in points below.
2. Many sentences may carry similar information with a tie of which one is really more important given other selected sentences are constant.
3. The meaning of sentences are vague w.r.t even some hints provided. [Typically, a summarizer provides hints as it learns, especially in case of RNN based mature models which learns as it works].

There are several uncertainty based techniques to solve uncertainty handling, these include Probability Theory, Fuzzy Logic, Rough Sets, and many of its variants and hybrids with techniques such as Neural Networks to mention a few.

So, we see that, Soft sets deal with uncertainty-based mechanisms to solve problems, and soft sets can hence be used to solve the problem of text summarization, which again can be viewed as an approximate learning task.

This article is introducing how a nice topic of research Soft Sets can be used with another topic of AI which is text summarization. However, experimental results have not been conducted. These are research ideas and we can guide you out in experimentation and analysis.

The formal definition of Soft sets goes as follows.

Definition 1: [Molodtsov 1999] A pair (F, E) is called a Soft Set over a universe under consideration U, if there is a mapping from the set E to P(U) the power set of U.

Soft sets define approximate learning. So, where does Text Summarization comes in? Well Text Summarization, weather is an extractive summarization or abstractive summarization are both having many shades of approximations and uncertainties. Let us understand it with a hypothetical representation of text with k sentence, namely s1 to s_k.

Let us consider the wordcloud of this text. From the world cloud we can define t1, t2…ti, i key phrases in the text, these may be the best way to define the text. In this word cloud, the key terms are the parameters defining the text.

For example the word cloud of the text in Appendix I is as follows:

When the keywords or phrases here form a set E then F can be defined as all those sentences which are related to these concepts.

Let E= {term1, term2, ..termk} form the above word cloud.

Then F of Soft set can be defined as, those sentence that are related to term1 from the wordcloud. These relations can be semantic and syntatic both.

F(term1)={sentence_i1, sentence_i1,….., sentence_ik}

These are all the sentences that define the concept of term1 in wordcloud.

And indeed F is a subset of Universe which is set of all sentences in consideration.

This is how we build the case study, in coming articles I shall explain how to go further in the with the algorithms.

Conclusion

We have defined a way to create a soft set for Text Summarization problem, next task remains is to actually solve the problem, and these hints shall be provided in upcoming articles.

## References

[Molodtsov 1999] Molodtsov, D. (1999). Soft set theory — first results. Computers & Mathematics with Applications37(4–5), 19–31.

## Appendix I

Text under consideration:

What Is Climate? How Is It Different From Weather?
You might know what weather is. Weather is the changes we see and feel outside from day to day.
It might rain one day and be sunny the next. Sometimes it is cold. Sometimes it is hot. Weather also changes from place to place.
People in one place might be wearing shorts and playing outside.
At the same time, people far away might be shoveling snow.
Climate is the usual weather of a place.
Climate can be different for different seasons.
A place might be mostly warm and dry in the summer.
The same place may be cool and wet in the winter.
Different places can have different climates.
You might live where it snows all the time.
And some people live where it is always warm enough to swim outside.
There’s also Earth’s climate.
Earth’s climate is what you get when you combine all the climates around the world together.
What Is Climate Change?
Climate change is a change in the usual weather found in a place.
This could be a change in how much rain a place usually gets in a year.
Or it could be a change in a place’s usual temperature for a month or season.
Climate change is also a change in Earth’s climate.
This could be a change in Earth’s usual temperature. Or it could be a change in where rain and snow usually fall on Earth.
Weather can change in just a few hours.
Climate takes hundreds or even millions of years to change.