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Vagueness — A rough set view

  • Games and Logic
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Structures in Logic and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1261))

Abstract

Vagueness for a long time has been studied by philosophers, logicians and linguists. Recently researchers interested in AI contributed essentially to this area.

In this paper we present a new approach to vagueness, called rough set theory. The starting of the theory theory is the assumption that fundamental mechanisms of human reasoning are based on the ability to classify object of interest, i.e. group objects into similarity classes, which form granules (basic concepts) of knowledge about the universe of discourse (e.g. color, height, weight etc.). Every union of basic concepts is called a precise (crisp) concept, otherwise the concept is called imprecise (rough). Thus rough concepts (sets) cannot be expressed in terms of elementary concepts (set). Therefore with each imprecise concept a pair of precise concepts, called its lower and upper approximation, is associated. Approximations are basic operations of rough set theory.

The paper contains basics of rough set theory, shows some of its applications, and the relationship to fuzzy sets, the theory of evidence, discriminant analysis and boolean reasoning methods are pointed out.

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  1. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Baltycka 5, 44 000, Gliwice, Poland

    Zdzislaw Pawlak

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  1. Zdzislaw Pawlak
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Jan Mycielski Grzegorz Rozenberg Arto Salomaa

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Pawlak, Z. (1997). Vagueness — A rough set view. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds) Structures in Logic and Computer Science. Lecture Notes in Computer Science, vol 1261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63246-8_7

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