Fuzzy rough sets and multiple-premise gradual decision rules
Salvatore Greco,Masahiro Inuiguchi,Roman Słowiński +2 more
- Vol. 41, Iss: 2, pp 179-211
TLDR
In this paper, a new fuzzy rough set approach is proposed, which does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication) to reduce the part of arbitrary in the fuzzy rough approximation.Abstract:
We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal properties of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand.read more
Citations
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Journal ArticleDOI
Rudiments of rough sets
Zdziasław Pawlak,Andrzej Skowron +1 more
TL;DR: The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.
Journal ArticleDOI
Rough sets and Boolean reasoning
Zdzisław Pawlak,Andrzej Skowron +1 more
TL;DR: Methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis are discussed.
Journal ArticleDOI
Modeling uncertainty in multi-criteria decision analysis
TL;DR: His paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain, and broadly survey the available decision models that can be used to support uncertain decision making.
Journal ArticleDOI
A rough set approach for the discovery of classification rules in interval-valued information systems
TL;DR: In this article, a rough set approach is proposed to discover classification rules through a process of knowledge induction which selects decision rules with a minimal set of features for classification of real-valued data.
Book ChapterDOI
Rough Set Based Decision Support
TL;DR: 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, in order to find concise classification patterns that agree with situations that are described by the data.
References
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Journal ArticleDOI
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TL;DR: This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.
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Rough sets theory for multicriteria decision analysis
TL;DR: The original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation, but is failing when preference-orders of attribute domains (criteria) are to be taken into account and it cannot handle inconsistencies following from violation of the dominance principle.