{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T10:59:48Z","timestamp":1784199588078,"version":"3.55.0"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,3,29]],"date-time":"2020-03-29T00:00:00Z","timestamp":1585440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Granular computing techniques are a huge discipline in which the basic component is to operate on groups of similar objects according to a fixed similarity measure. The first references to the granular computing can be seen in the works of Zadeh in fuzzy set theory. Granular computing allows for a very natural modelling of the world. It is very likely that the human brain, while solving problems, performs granular calculations on data collected from the senses. The researchers of this paradigm have proven the unlimited possibilities of granular computing. Among other things, they are used in the processes of classification, regression, missing values handling, for feature selection, and as mechanisms of data approximation. It is impossible to quote all methods based on granular computing\u2014we can only discuss a selected group of techniques. In the article, we have presented a review of recently developed granulation techniques belonging to the family of approximation algorithms founded by Polkowski\u2014in the framework of rough set theory. Starting from the basic Polkowski\u2019s standard granulation, we have described further developed by us concept dependent, layered, and epsilon variants, and our recent homogeneous granulation. We are presenting simple numerical examples and samples of research results. The effectiveness of these methods in terms of decision system size reduction and maintenance of the internal knowledge from the original data are presented. The reduction in the number of objects in our techniques while maintaining classification efficiency reaches 90 percent\u2014for standard granulation with usage of a kNN classifier (we achieve similar efficiency for the concept-dependent technique for the Naive Bayes classifier). The largest reduction achieved in the number of exhaustive set of rules at the efficiency level to the original data are 99 percent\u2014it is for concept-dependent granulation. In homogeneous variants, the reduction is less than 60 percent, but the advantage of these techniques is that it is not necessary to look for optimal granulation parameters, which are selected dynamically. We also describe potential directions of development of granular computing techniques by prism of described methods.<\/jats:p>","DOI":"10.3390\/a13040079","type":"journal-article","created":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T13:27:19Z","timestamp":1585661239000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["About Granular Rough Computing\u2014Overview of Decision System Approximation Techniques and Future Perspectives"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5508-9856","authenticated-orcid":false,"given":"Piotr","family":"Artiemjew","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, 10-710 Olsztyn, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,29]]},"reference":[{"key":"ref_1","unstructured":"Zadeh, L.A. (2020, February 13). Fuzzy Sets and Information Granularity. Available online: https:\/\/digitalassets.lib.berkeley.edu\/techreports\/ucb\/text\/ERL-m-79-45.pdf."},{"key":"ref_2","unstructured":"Zadeh, L.A. (2006, January 10\u201312). Graduation and granulation are keys to computation with information described in natural language. Proceedings of the 2006 IEEE International Conference on Granular Computing, Atlanta, GA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inform. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lin, T.Y., and Cercone, N. (1997). Synthesis of decision systems from data tables. Rough Sets and Data Mining, Springer.","DOI":"10.1007\/978-1-4613-1461-5"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lin, T.Y. (2005, January 25\u201327). Granular computing: Examples, intuitions and modeling. Proceedings of the 2005 IEEE International Conference on Granular Computing, Beijing, China.","DOI":"10.1109\/GRC.2005.1547232"},{"key":"ref_6","unstructured":"Yao, Y.Y. (2000, January 27). Granular computing: Basic issues and possible solutions. Proceedings of the 5th Joint Conference on Information Sciences, Atlantic, NJ, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pal, S.K., Polkowski, L., and Skowron, A. (2004). Information Granulation and Approximation in a Decision-Theoretical Model of Rough Sets. Rough-Neural Computing, Springer.","DOI":"10.1007\/978-3-642-18859-6"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yao, Y. (2005, January 25\u201327). Perspectives of granular computing. Proceedings of the 2005 IEEE International Conference on Granular Computing, Beijing, China.","DOI":"10.1109\/GRC.2005.1547239"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1002\/1098-111X(200101)16:1<57::AID-INT6>3.0.CO;2-Y","article-title":"Information granules: Towards foundations of granular computing","volume":"16","author":"Skowron","year":"2001","journal-title":"Int. J. Intell. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pal, S.K., Polkowski, L., and Skowron, A. (2004). Information Granules and Rough-Neural Computing. Rough-Neural Computing, Springer.","DOI":"10.1007\/978-3-642-18859-6"},{"key":"ref_11","first-page":"379","article-title":"On rough set logics based on similarity relations","volume":"64","author":"Polkowski","year":"2005","journal-title":"Fund. Inform."},{"key":"ref_12","first-page":"92","article-title":"Theoretical study of granular computing","volume":"Volume 4062","author":"Wang","year":"2006","journal-title":"Rough Sets and Knowledge Technology"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105930","DOI":"10.1016\/j.asoc.2019.105930","article-title":"Estimating incomplete information in group decision-making: A framework of granular computing","volume":"86","author":"Cabrerizo","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.asoc.2014.11.024","article-title":"Bayesian analysis of time series using granular computing approach","volume":"47","author":"Hryniewicz","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Martino, A., Giuliani, A., and Rizzi, A. (2019). (Hyper) Graph Embedding and Classification via Simplicial Complexes. Algorithms, 12.","DOI":"10.3390\/a12110223"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107187","DOI":"10.1016\/j.compbiolchem.2019.107187","article-title":"Metabolic networks classification and knowledge discovery by information granulation","volume":"84","author":"Martino","year":"2020","journal-title":"Comput. Biol. Chem."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Pownuk, A., and Kreinovich, V. (2019). Granular approach to data processing under probabilistic uncertainty. Granular Computing, Springer.","DOI":"10.1007\/s41066-019-00210-5"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.asoc.2016.05.006","article-title":"Granular data imputation: A framework of granular computing","volume":"46","author":"Zhong","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.knosys.2017.07.023","article-title":"Combining granular computing technique with deep learning for service planning under social manufacturing contexts","volume":"143","author":"Leng","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.2166\/wst.2020.006","article-title":"Granular computing-neural network model for prediction of longitudinal dispersion coefficients in rivers","volume":"80","author":"Ghiasi","year":"2020","journal-title":"Water Sci. Technol."},{"key":"ref_21","unstructured":"Capizzi, G., Lo Sciuto, G., Napoli, C., Po\u0142ap, D., and Wo\u017aniak, M. (2020, February 13). Small Lung Nodules Detection Based on Fuzzy-Logic and Probabilistic Neural Network with Bio-inspired Reinforcement Learning. Available online: https:\/\/ieeexplore.ieee.org\/abstract\/document\/8895990."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Polkowski, L. (2005, January 25\u201327). Formal granular calculi based on rough inclusions. Proceedings of the 2005 IEEE Conference on Granular Computing, Beijing, China.","DOI":"10.1109\/GRC.2005.1547235"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Polkowski, L. (2011). Approximate Reasoning by Parts. An Introduction to Rough Mereology, Springer.","DOI":"10.1007\/978-3-642-22279-5"},{"key":"ref_24","unstructured":"Polkowski, L. (2006, January 10). A model of granular computing with applications. Proceedings of the 2006 IEEE Conference on Granular Computing, Atlanta, GA, USA."},{"key":"ref_25","unstructured":"Artiemjew, P. (2020, February 13). Classifiers from Granulated Data Sets: Concept Dependent and Layered Granulation. Available online: https:\/\/pdfs.semanticscholar.org\/e46a\/0e41d0833263220680aa1ec7ae9ed3edbb42.pdf#page=7."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Artiemjew, P., and Ropiak, K.K. (2020). On Granular Rough Computing: Handling Missing Values by Means of Homogeneous Granulation. Computers, 9.","DOI":"10.3390\/computers9010013"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/978-3-540-73451-2_9","article-title":"Granulation of knowledge in decision systems: The approach based on rough inclusions. The method and its applications","volume":"Volume 4585","author":"Kryszkiewicz","year":"2007","journal-title":"Rough Sets and Intelligent Systems Paradigms"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Meyers, R.A. (2009). Granulation of Knowledge: Similarity Based Approach in Information and Decision Systems. Encyclopedia of Complexity and System Sciences, Springer.","DOI":"10.1007\/978-0-387-30440-3"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/978-3-540-73451-2_29","article-title":"On granular rough computing with missing values","volume":"Volume 4585","author":"Kryszkiewicz","year":"2007","journal-title":"Rough Sets and Intelligent Systems Paradigms"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Polkowski, L., and Artiemjew, P. (2015). Granular Computing in Decision Approximation - An Application of Rough Mereology, Springer.","DOI":"10.1007\/978-3-319-12880-1"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1007\/978-3-540-73451-2_30","article-title":"On granular rough computing: Factoring classifiers through granular structures","volume":"Volume 4585","author":"Kryszkiewicz","year":"2007","journal-title":"Rough Sets and Intelligent Systems Paradigms"},{"key":"ref_32","unstructured":"Artiemjew, P., and Ropiak, K. (2020, February 13). A Novel Ensemble Model - The Random Granular Reflections. Available online: http:\/\/ceur-ws.org\/Vol-2240\/paper17.pdf."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ropiak, K., and Artiemjew, P. (2019). Homogenous Granulation and Its Epsilon Variant. Computers, 8.","DOI":"10.3390\/computers8020036"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/978-3-642-30341-8_4","article-title":"A Review of the Knowledge Granulation Methods: Discrete vs. Continuous Algorithms","volume":"Volume 43","author":"Skowron","year":"2013","journal-title":"Rough Sets and Intelligent Systems - Professor Zdzis\u0142aw Pawlak in Memoriam"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Polkowski, L. (2002). Rough Sets, Springer.","DOI":"10.1007\/978-3-7908-1776-8"},{"key":"ref_36","unstructured":"Quinlan, J.R. (2004). C4.5: Programs for Machine Learning, Elsevier."},{"key":"ref_37","unstructured":"(2020, February 13). University of California, Irvine Machine Learning Repository. Available online: https:\/\/archive.ics.uci.edu\/ml\/index.php."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/978-3-319-25783-9_23","article-title":"The Rough Granular Approach to Classifier Synthesis by Means of SVM","volume":"Volume 9437","author":"Yao","year":"2015","journal-title":"Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ropiak, K., and Artiemjew, P. (2020). On a Hybridization of Deep Learning and Rough Set Based Granular Computing. Algorithms, 13.","DOI":"10.3390\/a13030063"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/4\/79\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:13:02Z","timestamp":1760173982000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/4\/79"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,29]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["a13040079"],"URL":"https:\/\/doi.org\/10.3390\/a13040079","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,29]]}}}