Journal ArticleDOI
A generalized definition of rough approximations based on similarity
TLDR
New definitions of lower and upper approximations are proposed, which are basic concepts of the rough set theory and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.Abstract:
This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.read more
Citations
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Journal ArticleDOI
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.
Book
Theory and practice of uncertain programming
TL;DR: This book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem.
Journal ArticleDOI
Neighborhood rough set based heterogeneous feature subset selection
TL;DR: A neighborhood rough set model is introduced to deal with the problem of heterogeneous feature subset selection and Experimental results show that the neighborhood model based method is more flexible to deals with heterogeneous data.
Journal ArticleDOI
Reduction and axiomization of covering generalized rough sets
William Zhu,Fei-Yue Wang +1 more
TL;DR: It has been proved that the reduct of a covering is the minimal covering that generates theSame covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining.
Journal ArticleDOI
Topological approaches to covering rough sets
TL;DR: This paper explores the topological properties of covering-based rough sets, studies the interdependency between the lower and the upper approximation operations, and establishes the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation.
References
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Journal ArticleDOI
Features of Similarity
TL;DR: The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds and a set of qualitative assumptions are shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features.
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Rough sets
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.
Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
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Semiorders and a Theory of Utility Discrimination
TL;DR: In this article, a class of intransitive indifference relations are admitted and axiomatized, which is substantially equivalent to a utility theory in which there are just noticeable difference functions which state for any value of utility the change in utility so that the change is just noticeable.