Biograph: Dr./IRSS Fellow/CAAI Fellow, Duoqian Miao is a Professor and the Vice
Director of the Key Laboratory of Embedded System and Service Computing of Ministry ofEducation, Tongji University, China. His research interests include Artificial Intelligence,
Machine Learning, Big Data Analysis, Granular Computing and Rough Sets. Since 1997, hehas published over 180 research papers (e.g., IEEE TKDE, IEEE TFS, IEEE TIFS, IEEE TC,
IEEE TIP, IEEE TCSVT) in refereed journals and conferences (e.g., AAAI, NeurIPS, ICPR,ICCV, WACV). In addition, he has published 10 academic books and over 20 patents. He
serves as AC of Information Sciences, International Journal of Approximate Reasoning,
CAAI Transactions on Intelligence Technology, and Chinese Journal of Computer Researchand Development, etc. He is the president of International Rough Sets Society (2020- 2022),
vice president of Shanghai Computer Federation(2018-2022), vice president of Shanghai
Association for Artificial Intelligence, Chair of Granular Computing and Knowledge
Discovery Technical Committee of CAAI(2012-2022) , a distinguished member of China
Computer Federation(CCF).
Title: The Contributions of Rough Set Theory to Artificial Intelligence
Abstract: After more than 70 years of development, artificial intelligence is moving towards
the stage of general artificial intelligence, which has a profound impact on human daily workand life. Rough set theory emerged in the early 1980s and, after 40 years of development, hasplayed an irreplaceable role in handling imprecise, inconsistent, and incomplete data [1]. As
we all know, artificial intelligence mainly studies knowledge representation, knowledge
acquisition, and knowledge application, which means that the research of artificial
intelligence revolves around knowledge. But what is knowledge? Unfortunately, textbooks on
artificial intelligence do not provide a formal definition of knowledge [2]. This report will
introduce the understanding and formal definition of knowledge in rough set theory, as wellas its significant contributions to artificial intelligence, hoping to provide inspiration for
future research in artificial intelligence.
The recent emergence of ChatGPT and Sora aroused the attention of large models, whichhas promoted the advent of general artificial intelligence [3,4]. As we stand on the precipiceof a new era in artificial intelligence, the foundational role of knowledge representation inboth acquisition and application cannot be overstated. Currently, the field leans towards
end-to-end methodologies characterized by simplification and automated computation forknowledge representation. However, this approach is not without its Achilles' heel: aconspicuous lack of interpretability. Knowledge acquisition, the technological linchpin for
extracting valuable insights from data, is predominantly facilitated by machine learningmodels, ranging from classical algorithms like K-Nearest Neighbors (KNN) and Support
Vector Machines (SVM) to the more contemporary deep learning paradigms. Furthermore,expert systems have emerged as pivotal instruments for the application of knowledge,
permeating various domains within the AI landscape. According to these developments, aformal definition of "knowledge" is not merely desirable but imperative for the continued
advancement of artificial intelligence.
Rough sets (RS), introduced by Z. Pawlak in 1982, offer an efficient approach forhandling imprecise, inconsistent, and incomplete data [1]. It provides formal knowledgerepresentation that is understood as the ability to classify objects. In this theory, theknowledge is analogized from knowledge to object partition and further equivalence relation,
which can be represented as 𝐾 = (𝑈, ℝ), where 𝑈 = {𝑥! , 𝑥" , ⋯ , 𝑥# } is the universe andℝ = {𝑅! , 𝑅" , ⋯ , 𝑅$ } is a family of equivalence relations [2]. This is an algebraic
representation of knowledge. Subsequently, attribute reduction based on positive region is
proposed to obtain an important feature subset. Nevertheless, it is only a decidable definition,and selecting a minimum subset is an NP-hard problem. To address this challenge, we haveproposed a heuristic algorithm for attribute reduction based on attribute significance [2].
Moreover, Skowron introduced the discernibility matrix for attribute reduction [5]. Similarly,
it is also a decidable definition. Consequently, we have developed a reduction algorithm thatis attuned to the attribute frequency within the discernibility matrix [2]. Crucially, we haveintroduced the information representation of knowledge and defined the lower and upper
approximation sets based on it. Some heuristic methods based on information entropy,conditional entropy, and mutual information are proposed for attribute reduction [2,6]. Morerecently, we integrated zentropy thought to define a zentropy-based uncertainty measure andhave adapted it to computing reductions [7]. According to the above analysis, we divided
these methods into algebraic representation and information representation, which can be seenin Fig. 1.

Fig.1 The relationship of knowledge representation in rough sets
Concept is the fundamental unit for the recognition and acquisition of knowledge [8]. In
machine intelligence, the processing of precise concepts often surpasses human capabilities.
Currently, how to handle imprecise concepts plays a vital role in artificial intelligence [9,10].
Philosophical scholars contend that a concept is imprecise if its boundary region is nonempty[11]. However, it is only a semantic limitation that cannot be recognized by computers, bringchallenges of imprecise concepts in computational recognition. Rough set theory provides amathematical framework for calculating the boundary region of imprecise concepts. It
approximates imprecise concepts by two precision sets (lower and upper approximatesets) and describes their uncertainty via boundary region [2,12,13]. Subsequently, the positive,negative, and boundary regions are induced by rough sets, and each region has different
actions. Based on this, three-way decision (3WD) is introduced by Y. Yao, which is anexploration of rough set theory and has successfully applied to various scenarios [14].
Rough set theory is an efficient machine learning model for processing qualitative data[15]. It provides a multi-granulation representation, learning, and reasoning methods forknowledge in artificial intelligence. In essence, rough set theory has made significant
contributions to AI through three pivotal aspects: the formal representation of knowledge, thecomputation of boundary regions for imprecise concepts, and the multi-granulation
knowledge representation and reasoning methods. As a holistic, data-driven model, rough set
theory shows robust potential prospects and developmental avenues in artificial intelligence.
References[1] Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences, vol.
11, pp. 341-356, 1982.
[2] D. Miao, Rough set theory and its applications in machine learning, Doctoral dissertation,
Institute of Automation, Chinese academy of sciences, 1997.
[3] J. Lechien, G. Briganti, L. Vaira, Accuracy of ChatGPT-3.5 and -4 in providing scientificreferences in otolaryngology-head and neck surgery, European Archives ofOto-Rhino-Laryngology, vol. 281, pp. 2159–2165, 2024.
[4] L. Fan, C. Guo, Y. Tian, et al., Sora for foundation robots with parallel intelligence: three
world models, three robotic systems, Frontiers of Information Technology & ElectronicEngineering, doi: https://doi.org/10.1631/FITEE.2400144, 2024.
[5] A. Skowron, R. Cecylia, The discernibility matrices and functions in information systems,
Intelligent decision support: handbook of applications and advances of the rough setstheory. Dordrecht: Springer Netherlands, pp. 331-362, 1992.
[6] K. Yuan, W. Xu, D. Miao, A local rough set method for feature selection by variable
precision composite measure, Applied Soft Computing, vol. 155, pp. 111450, 2024.
[7] K. Yuan, D. Miao, Y. Yao, et al., Feature selection using zentropy-based uncertainty
measure, IEEE Transactions on Fuzzy Systems, vol. 32, no. 4, pp. 2246-2260, 2024.
[8] D. Guo, W. Xu, W. Ding, et al., Concept-cognitive learning survey: mining and fusing
knowledge from data, Information Fusion, vol. 109, pp. 102426, 2024.
[9] D. Slezak, R. Glick, P. Betliski, et al., A new approximate query engine based onintelligent capture and fast transformations of granulated data summaries, Journal ofIntelligent Information Systems, vol. 50, pp. 385C414, 2018.
[10] Y. Yao, Interval-set algebra for qualitative knowledge representation, the 5thInternational Conference on Computing and Information, pp. 370-375, 1993.
[11] F. Ramsey, Review of Ludwig Wittgenstein's "Tractatus Logico-Philosophicus", Mind,
vol. 32, no. 128, pp. 465-478, 1923.
[12] P. Lingras, M. Chen, D. Miao, Rough cluster quality index based on decision theory,
IEEE Transactions on Knowledge and Data Engineering, vol. 21, pp. 1014-1026, 2009.
[13] J. Yao, A. Vasilakos, W. Pedrycz, Granular computing: perspectives and challenges, IEEE
Transactions on Cybernetics, vol. 43, no. 6, pp. 1977-1989, 2013.
[14] Y. Yao, Three-way decisions with probabilistic rough sets, Information sciences, vol.
180, no. 3, pp.341-353, 2010.
[15] D. Miao, Y. Zhao, Y. Yao, et al., Relative reducts in consistent and inconsistent decisiontables of the Pawlak rough set model, Information Sciences, vol. 179, no. 24, pp.
4140-4150, 2009.