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Some Foundational Aspects of Rough Sets Rendering Its Wide Applicability

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Rough Sets (IJCRS 2018)

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Abstract

This paper aims to discuss about the reasons behind the wide applicability of the rough set approach in real-life projects. The rough set-based approximations of (vague) concepts is one among the most central notions, available in the literature, for dealing with imperfect data and/or information. Moreover, as the approach based on rough sets is directly driven from data it turns out to be advantageous for real life projects where data plays a crucial role. Besides, using rough set approach one can deal efficiently with algorithmic issues, especially in the context of searching for relevant computational building blocks (granules) for approximation of complex vague concepts. In this paper, we would focus on these few aspects of rough sets, in order to explain its wide applicability in real-life projects.

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Notes

  1. 1.

    For more information readers are referred to some survey papers [55,56,57, 67], books, e.g., [19, 57, 71] and to the rough set database rsds.univ.rzeszow.pl.

  2. 2.

    This stage started a few years after the first paper by Pawlak on rough sets was published.

  3. 3.

    Leslie Valiant: https://people.seas.harvard.edu/~valiant/researchinterests.htm.

  4. 4.

    where U is a finite set and A is a set of attributes (i.e., for any \(a\in A,\) \(a: U\longrightarrow V_a,\) where \(V_a\) is the set of values of a).

  5. 5.

    \(\left| {X}\right| \) denotes the cardinality of the set X.

  6. 6.

    If then we will also write \(\Vert \alpha \Vert _U\) instead of .

  7. 7.

    Let us recall that a decision system is a triplet (U, A, d),  where (U, A) is an information system and \(d:U\longrightarrow V_d\) is the decision attribute with the set of values \(V_d\) such that \(d\notin A\) [51].

  8. 8.

    A rule of the form \(lh(r)\longrightarrow d=i, \) where lh(r) is a conjunction of descriptors of the form \(a=v\) for some \(a\in A_{tr}\) and \(i\in \{0,1\}\) is minimal if this rule is true in \(U_{tr}\) but if we drop an arbitrary descriptor from lh(r) the obtained rule will be no longer true in \(U_{tr}\) [39, 55].

  9. 9.

    The readers are referred to the literature for other relationships of rough sets and Dempster-Shafer theory (see, e.g., [11, 12, 76, 79, 10]). For example, new methods of inducing rules were developed for searching rules with the large support for unions of few decision classes and eliminating many other decision classes (see, e.g., [33]).

  10. 10.

    https://people.seas.harvard.edu/~valiant/researchinterests.htm.

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Acknowledgments

The authors would like to thank Professor Mihir Chakraborty for suggesting the problem considered in this paper.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  2. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Andrzej Skowron

  3. Vistula University, Stokłosy 3, 02-787, Warsaw, Poland

    Soma Dutta

  4. Department of Mathematics and Computer Science, University of Warmia and Mazury, Sloneczna str. 54, 10-710, Olsztyn, Poland

    Soma Dutta

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  1. Andrzej Skowron
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Editors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Hung Son Nguyen

  2. Faculty of Information Technology, Vietnam National University, Hanoi, Vietnam

    Quang-Thuy Ha

  3. School of Information Science, Southwest Jiaotong University, Chengdu, China

    Tianrui Li

  4. Institute of Computer Science, University of Silesia, Sosnowiec, Poland

    Małgorzata Przybyła-Kasperek

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Skowron, A., Dutta, S. (2018). Some Foundational Aspects of Rough Sets Rendering Its Wide Applicability. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_3

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