Fuzzy set extensions of the dominance-based rough set approach

Salvatore Greco, B. Matarazzo, R. Slowinski

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

    Abstract

    Rough set theory has been proposed by Pawlak in the early 80s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects described by a set Q of condition and decision attributes. Decision attributes make a partition of U into decision classes. Basic concepts of rough set theory are: indiscernibility relation on U, lower and upper (rough) approximations of decision classes, dependence and reduction of attributes from Q, and decision rules induced from rough approximations of decision classes. The original rough set idea was failing, however, to handle preferential ordering of domains of attributes (scales of criteria), as well as preferential ordering of decision classes. In order to deal with multiple criteria decision problems a number of methodological changes to the original rough set theory were necessary. The main change is the substitution of the indiscernibility relation by a dominance relation, which permits approximation of ordered sets. In multiple criteria decision context, the information table is composed of decision examples given by a decision maker. The Dominance-based Rough Set Approach (DRSA) applied to this information table results with a set of decision rules, being a preference model of the decision maker. It is more general than the classical multiple attribute utility model or outranking model, and it is more understandable because of its natural syntax. In this chapter, after recalling the classical rough set approach and DRSA, we review their fuzzy set extensions. Moreover, we characterize the dominance-based rough approximation of a fuzzy set, and we show that the classical rough approximation of a crisp set is its particular case. In this sense, DRSA is also relevant in the case where preferences are not considered, but just a kind of monotonicity relating values of different attributes is meaningful for the analysis of data at hand. In general terms, monotonicity concerns relationship between different aspects of a phenomenon described by data: for example, "the larger the house, the higher its price" or "the closer the house to the city centre, the higher its price". In this perspective, DRSA gives a very general framework for reasoning about data using only monotonicity relationships.
    Original languageEnglish
    Title of host publicationFuzzy sets and their extensions: representation, aggregation and models
    EditorsH. Bustince, F. Herrera, J. Montero
    Place of PublicationBerlin
    PublisherSpringer
    Pages239-261
    Number of pages23
    Volume220
    Edition220
    ISBN (Print)9783540737223
    DOIs
    Publication statusPublished - 2008

    Publication series

    NameStudies in fuzziness and soft computing
    PublisherSpringer
    Number220

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