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Rough-Set-Based Decision Support

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Abstract

In this chapter, we are concerned with the discovery of knowledge from data describing a decision situation. A decision situation is characterized by a set of states or examples, which relate the input with the output of the situation. The aim is to find concise knowledge patterns that summarize a decision situation, and that are useful for explanation of this situation, as well as for the prediction of future similar situations. They are particularly useful in such decision problems as technical or medical diagnostics, performance evaluation and risk assessment. A decision situation is described by a set of attributes, which we might also call properties, features, characteristics, etc. Such attributes may be concerned with either the input or output of a situation or, in other words, with either conditions or decisions. Within this chapter, we will refer to states or examples of a decision situation as objects. The goal of the chapter is to present a knowledge discovery paradigm for multi-attribute and multicriteria decision making, which is based upon the concept of rough sets. Rough set theory was introduced by Pawlak (1982, 1991). Since then, it has often proved to be an excellent mathematical tool for the analysis of a vague description of objects. The adjective vague (referring to the quality of information) is concerned with inconsistency or ambiguity. The rough set philosophy is based on the assumption that with every object of the universe U there is associated a certain amount of information (data, knowledge). This information can be expressed by means of a number of attributes. The attributes describe the object. Objects which have the same description are said to be indiscernible (similar) with respect to the available information. The indiscernibility relation thus generated constitutes the mathematical basis of rough set theory. It induces a partition of the universe into blocks of indiscernible objects, called elementary sets, which can then be used to build knowledge about a real or abstract world. The use of the indiscernibility relation results in information granulation.

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Notes

  1. 1.

    The new material added to the first edition of this chapter is taken from our survey published in Slowinski et al. (2012), with kind permission of the Brazilian Society of Operations Research (SOBRAPO).

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Authors and Affiliations

  1. Institute of Computing Science, Poznań University of Technology, Poznań, and Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

    Roman Słowiński

  2. Department of Economics and Business, University of Catania, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo

  3. Portsmouth Business School, Operations & Systems Management University of Portsmouth, Portsmouth, PO1 3DE, UK

    Salvatore Greco

Authors
  1. Roman Słowiński
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  2. Salvatore Greco
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  3. Benedetto Matarazzo
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Correspondence to Roman Słowiński .

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Editors and Affiliations

  1. Computing Science and Mathematics, University of Stirling, Scotland, United Kingdom

    Edmund K. Burke

  2. Research and Knowledge Transfer, University of Nottingham, Malaysia & UK, Semenyih, Malaysia

    Graham Kendall

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Słowiński, R., Greco, S., Matarazzo, B. (2014). Rough-Set-Based Decision Support. In: Burke, E., Kendall, G. (eds) Search Methodologies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6940-7_19

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