A generalization of the indiscernibility relation for rough set analysis of quantitative information

  • R. Slowinski
Article

Abstract

Rough set theory is a formal tool for analysis of knowledge gained by experience. The knowledge is represented by a data set organized in a table called information system. Rows of the table correspond to objects and columns to attributes. The idea of the rough set consists in approximation of a set of objects by a pair of sets called lower and upper approximation. The definition of the approximations follows from an indiscernibility relation between objects. Objects are described by attributyes of qualitative or quantitative nature. In the case of quantitative atrributes, the indiscrenibility relation has been defined after partition of the real scale into a finite number of intervals. The bounds of the intervals are more or less arbitrary and may influence the result of the rough set analysis. In order to capture this influence, we consider overlapped intervals and introduce for them a strict and a weak indiscernibility relation. Then, we generalize the lower and upper approximations, the measures of the quality of approximation and the concept of decision rules.

Keywords

Rough set theory knowledge analysis information system indiscemibility relation among objects 

Riassunto

Nella teoria degli insiemi apprissimati, la relazione di indiscemibilità trao oggetti costituisce il punto di partenza della definizione della coppia di insiemi, chiamati rispettivamente approssimazione superiore ed inferiore, che caratterizzano ciascun insieme. Se gli oggetti sono descritti mediante atributi di natura quantitativa, occorre suddividere il dominio di ciascuno di questi in sottointervalli, mediante l'introduzione di opportuni confini. Per analizzare l'effetto dell'arbitrarietà della scelta di tali valori, si introducono delle soglie additive e si considerano le zone di sovrapposizione di tali sottointervalli, definendo opportunamente relazioni di indiscemibilità forte e debole. Siggene ralizzano quindi i concetti di approssimazione superiore ed infereiore, gli indicaartori della qualità dell'approssimazione e le regole decisionali stesse, fornendone un'esemplificazione applicativa.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • R. Slowinski
    • 1
  1. 1.Institute of Computing ScienceTechnical University of PoznanPoznanPoland

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