Rough set theory, introduced by Zdzisław Pawlak in the early 1980s, is a mathematical tool designed to handle vagueness and uncertainty. It is particularly useful in artificial intelligence (AI) and cognitive sciences, including machine learning, knowledge acquisition, decision analysis, and pattern recognition. The theory does not require additional information about data, such as probability distributions, making it more flexible than other methods like the Dempster-Shafer theory or fuzzy set theory. The core concepts of rough set theory involve the use of lower and upper approximations to define sets of objects that are indiscernible based on a set of attributes. This allows for the identification of redundant attributes and the computation of reducts, which are minimal sets of attributes that define the same indiscernibility relation. The theory also introduces the concepts of lower and upper approximations of concepts, which help in dealing with inconsistencies and uncertainty. Rough set theory has been applied in various fields, including medicine, business, engineering, and environmental science. It has been used for data reduction, discovery of data dependencies, decision-making, and pattern recognition. Notable applications include the development of expert systems, enhancing facility compliance, and predicting preterm birth in pregnant women. The theory has also been integrated into machine learning systems like LERS (Learning from Examples based on Rough Sets), which can induce rules from data and classify new examples. Additionally, rough set methods have been used in decision analysis, knowledge discovery in databases (KDD), and technical diagnostics. Despite its practical success, rough set theory still faces theoretical challenges, particularly in areas such as rough logic, neural networks, and genetic algorithms. Future research aims to address these challenges and further explore the theory's potential in various applications.Rough set theory, introduced by Zdzisław Pawlak in the early 1980s, is a mathematical tool designed to handle vagueness and uncertainty. It is particularly useful in artificial intelligence (AI) and cognitive sciences, including machine learning, knowledge acquisition, decision analysis, and pattern recognition. The theory does not require additional information about data, such as probability distributions, making it more flexible than other methods like the Dempster-Shafer theory or fuzzy set theory. The core concepts of rough set theory involve the use of lower and upper approximations to define sets of objects that are indiscernible based on a set of attributes. This allows for the identification of redundant attributes and the computation of reducts, which are minimal sets of attributes that define the same indiscernibility relation. The theory also introduces the concepts of lower and upper approximations of concepts, which help in dealing with inconsistencies and uncertainty. Rough set theory has been applied in various fields, including medicine, business, engineering, and environmental science. It has been used for data reduction, discovery of data dependencies, decision-making, and pattern recognition. Notable applications include the development of expert systems, enhancing facility compliance, and predicting preterm birth in pregnant women. The theory has also been integrated into machine learning systems like LERS (Learning from Examples based on Rough Sets), which can induce rules from data and classify new examples. Additionally, rough set methods have been used in decision analysis, knowledge discovery in databases (KDD), and technical diagnostics. Despite its practical success, rough set theory still faces theoretical challenges, particularly in areas such as rough logic, neural networks, and genetic algorithms. Future research aims to address these challenges and further explore the theory's potential in various applications.