Rudiments of rough sets

By Zdzislaw Pawlak, Andrzej Skowron. Information Sciences, 2007

2,165 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Information Systems

View Paper: https://www.semanticscholar.org/paper/42804de301f3ff3300c70f42e138274524de75db

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In Artificial Intelligence

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Citations in the corpus

Three-Way Decision: An Interpretation of Rules in Rough Set Theory (2009, background): “An important application of rough set theory is to induce classification or decision rules that indicate the decision class of an object based on its values on some condition attributes [6,8].”
Incomplete Multigranulation Rough Set (2010, methodology): “Rough-set theory, proposed by Pawlak and Skowron [24], [26], has become a well-established mechanism for uncertainty management in a wide variety of applications related to artificial intelligence [4], [11], [12], [17], [43], [44], [58].”
Multisensor data fusion: A review of the state-of-the-art (2013, methodology): “The approximation is represented as a tuple hB⁄(T),B⁄(T)i, where B⁄(T) and B⁄(T) represent the lower and upper approximations of set T within frame FB, repectively, and are defined as below [74]”
Three-way decisions with probabilistic rough sets (2010, background): “Since the introduction of rough sets more than a quarter century ago [14], researchers have accumulated a vast literature on its theory and applications [17,18,24].”
Soft sets combined with fuzzy sets and rough sets: a tentative approach (2010, methodology): “Conventionally, we refer to R as an indiscernibility relation ( Pawlak and Skowron 2007 )f or the reason that it is often obtained from an information system (see Definition 1) and gives a partition of U due to the indiscernibility of objects in U .F orx; y 2 U; x and y are said to be R-indiscernib”
AI Agents vs. Agentic AI: A Conceptual Taxonomy, Applications and Challenges (2025, neutral): “Some systems integrate basic learning capabilities [72] through feed-back loops [73,74], heuristics [75], or updated context buffers to refine behavior over time, particularly in settings like personalized recommendations or conversation flow management [76– 78].”
Soft semirings (2008, background): “Alternatively, mathematical theories such as probability theory, fuzzy set theory [1,2], rough set theory [3,4], vague set theory [5] and the interval mathematics [6] were established by researchers to modelling uncertainties appearing in the above fields.”
Soft sets and soft rough sets (2011, background): “[23] An information system (or a knowledge representation system) is a pair I 1⁄4 ðU;AÞ of non-empty finite sets U and A, where U is a set of objects and A is a set of attributes; each attribute a 2 A is a function a:U ? Va, where Va is the set of values (called domain) of attribute a.”
Granular Computing: Perspectives and Challenges (2013, background): “Rough sets [51]–[54], [56] emphasize a roughness of description of a given concept X when being realized in terms of the indiscernibility relation provided in advance.”
Positive approximation: An accelerator for attribute reduction in rough set theory (2010, background): “Rough set theory by Pawlak [33–36] is a relatively new soft computing tool for the analysis of a vague description of an object, and has become a popular mathematical framework for pattern recognition, image processing, feature selection, neurocomputing, data mining and knowledge discovery from larg”
MGRS: A multi-granulation rough set (2010, background): “Yao [38] connected rough set approximation with a classic distance measure based on sets, called Marczewski–Steinhaus metric (MZ), which is defined by MZðX; YÞ ¼ jX [ Yj À jX \ Yj jX [ Yj : Gediga and Düntsch [3] redefined the measures a; c and p using MZ, which discovers the relationships between t”
Decision-Theoretic Rough Set Models (2007, background): “Ever since the introduction of rough set theory by Pawlak in 1982 [10, 11, 13], many proposals have been made to incorporate probabilistic approaches into the theory [14, 29–31].”