{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T01:34:35Z","timestamp":1768008875123,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,22]],"date-time":"2023-04-22T00:00:00Z","timestamp":1682121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["12071271"],"award-info":[{"award-number":["12071271"]}]},{"name":"National Science Foundation of China","award":["11671244"],"award-info":[{"award-number":["11671244"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Knowledge discovery through spatial and temporal aspects of data related to occurrences of events has many applications in digital forensics. Specifically, in electronic surveillance, it is helpful to construct a timeline to analyze information. The existing techniques only analyze the occurrence and co-occurrence of events; however, in general, there are three aspects of events: occurrences (and co-occurrences), nonoccurrences, and uncertainty of occurrences\/non-occurrences with respect to spatial and temporal aspects of data. These three aspects of events have to be considered to better analyze periodicity and predict future events. This study focuses on the spatial and temporal aspects given in intuitionistic fuzzy (IF) datasets using the granular computing (GrC) paradigm; formal concept analysis (FCA) was used to understand the granularity of data. The originality of the proposed approach is to discover the periodicity of events data given in IF sets through FCA and the GrC paradigm that helps to predict future events. An experimental evaluation was also performed to understand the applicability of the proposed methodology.<\/jats:p>","DOI":"10.3390\/axioms12050407","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T02:31:05Z","timestamp":1682303465000},"page":"407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Granular Computing Approach to Evaluate Spatio-Temporal Events in Intuitionistic Fuzzy Sets Data through Formal Concept Analysis"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8795-7512","authenticated-orcid":false,"given":"Imran","family":"Ali","sequence":"first","affiliation":[{"name":"College of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China"},{"name":"Department of Computer Science, Sukkur IBA University, Airport Road, Sukkur 65200, Pakistan"}]},{"given":"Yongming","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China"}]},{"given":"Witold","family":"Pedrycz","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6R 2G7, Canada"},{"name":"Systems Research Institute, Polish Academy of Sciences, 01-224 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s41066-020-00232-4","article-title":"Spatial and temporal reasoning with granular computing and three way formal concept analysis","volume":"6","author":"Gaeta","year":"2021","journal-title":"Granul. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.ins.2014.12.010","article-title":"Concept learning via granular computing: A cognitive viewpoint","volume":"298","author":"Li","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1007\/s13042-013-0150-z","article-title":"On rule acquisition in decision formal contexts","volume":"4","author":"Li","year":"2013","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/TCYB.2014.2361772","article-title":"Granular Computing Approach to Two-Way Learning Based on Formal Concept Analysis in Fuzzy Datasets","volume":"46","author":"Xu","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1109\/TCYB.2014.2371476","article-title":"Granular Transformation and Irreducible Element Judgment Theory Based on Pictorial Diagrams","volume":"46","author":"Wei","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_6","unstructured":"Zhou, J., Yang, S., Wang, X., and Liu, W. (2021). Granule Description based on Compound Concepts. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ins.2020.06.020","article-title":"Local temporal-spatial multi-granularity learning for sequential three-way granular computing","volume":"541","author":"Yang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1007\/s13042-021-01426-1","article-title":"A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system","volume":"13","author":"Xin","year":"2022","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1007\/s00500-020-05268-x","article-title":"Spatial\u2013temporal fuzzy information granules for time series forecasting","volume":"25","author":"Zhao","year":"2021","journal-title":"Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Cui, J., and Zhao, J. (2021). Optimal route planning of traffic multi-source route based on granular computing. J. Ambient Intell. Humaniz. Comput., 1\u201311.","DOI":"10.1007\/s12652-020-02815-0"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s41066-015-0008-8","article-title":"Bridging gaps between several forms of granular computing","volume":"1","author":"Dubois","year":"2016","journal-title":"Granul. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sang, B., Long, B., Pang, J., and Xu, W. (2019). The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context. Entropy, 21.","DOI":"10.3390\/e21030262"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.1016\/j.ins.2010.03.019","article-title":"Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology","volume":"181","author":"Bloch","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pang, J., Zhang, X., and Xu, W. (2013). Attribute Reduction in Intuitionistic Fuzzy Concept Lattices. Abs. App. Anal., 22\u201324.","DOI":"10.1155\/2013\/271398"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_17","first-page":"142","article-title":"Intuitionistic Fuzzy Sets","volume":"35","author":"Atanassov","year":"1999","journal-title":"Stud. Fuzziness Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Atanassov, K.T. (2012). On Intuitionistic Fuzzy Sets Theory, Springer. [1st ed.].","DOI":"10.1007\/978-3-642-29127-2"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Szmidt, E., and Kacprzyk, J. (2006, January 4\u20136). Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. Proceedings of the 2006 3rd International IEEE Conference Intelligent Systems, London, UK.","DOI":"10.1109\/IS.2006.348507"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Szmidt, E. (2014). Distances and Similarities in Intuitionistic Fuzzy Sets, Springer. [1st ed.].","DOI":"10.1007\/978-3-319-01640-5"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3057","DOI":"10.3233\/IFS-152031","article-title":"A new definition and formula of entropy for intuitionistic fuzzy sets","volume":"30","author":"Zhu","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"563745","DOI":"10.1155\/2015\/563745","article-title":"Entropy Measures for Interval-Valued Intuitionistic Fuzzy Sets and Their Application in Group Decision-Making","volume":"2015","author":"Wei","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/9781119544203.ch9","article-title":"Application of Fuzzy\/Intuitionistic Fuzzy Set in Image Processing","volume":"9","author":"Chaira","year":"2019","journal-title":"Fuzzy Set Its Ext."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Faizi, S., Sa\u0142abun, W., Rashid, T., Zafar, S., and Watr\u00f3bski, J. (2020). Intuitionistic fuzzy sets in multi-criteria group decision making problems using the characteristic objects method. Symmetry, 12.","DOI":"10.3390\/sym12091382"},{"key":"ref_25","unstructured":"Bujnowski, P., Szmidt, E., and Kacprzyk, J. (2014, January 24\u201326). Intuitionistic Fuzzy Decision Tree: A New Classifier. Proceedings of the 7th IEEE International Conference Intelligent Systems IS\u20192014, Warsaw, Poland."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.eswa.2015.10.026","article-title":"An efficient algorithm for increasing the granularity levels of attributes in formal concept analysis","volume":"46","author":"Zou","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_27","first-page":"38","article-title":"Granular Computing\u2014The Emerging Paradigm","volume":"1","author":"Pedrycz","year":"2007","journal-title":"J. Uncertain Syst."},{"key":"ref_28","first-page":"85","article-title":"Granular computing, Announcement of the BISC Special Interest Group on Granular Computing","volume":"1","author":"Lin","year":"2005","journal-title":"IEEE Int. Con. Gr. Comp."},{"key":"ref_29","first-page":"107","article-title":"Neutrosophic Set\u2014A Generalization of the Intuitionistic Fuzzy Set","volume":"1","author":"Smarandache","year":"2010","journal-title":"J. Def. Resour. Manag. (JoDRM)"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Pedrycz, W. (2021). An Introduction to Computing with Fuzzy Sets, Springer. [1st ed.].","DOI":"10.1007\/978-3-030-52800-3"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2018.01.032","article-title":"Towards a granular computing approach based on Formal Concept Analysis for discovering periodicities in data","volume":"146","author":"Loia","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TFUZZ.2018.2862870","article-title":"Intuitionistic Fuzzy Rough Set-Based Granular Structures and Attribute Subset Selection","volume":"27","author":"Tan","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhou, L. (2010, January 10\u201312). Formal concept analysis in intuitionistic fuzzy formal context. Proceedings of the 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery 2010, Yantai, China.","DOI":"10.1109\/FSKD.2010.5569658"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1007\/s13042-020-01243-y","article-title":"Entropy based optimal scale combination selection for generalized multi-scale information tables","volume":"12","author":"Bao","year":"2021","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"607","DOI":"10.14311\/NNW.2016.26.035","article-title":"Attribute significance, consistency measure and attribute reduction in formal concept analysis","volume":"26","author":"Huang","year":"2016","journal-title":"Neural Netw. World"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2303","DOI":"10.3390\/e15062303","article-title":"An entropy-based weighted concept lattice for merging multi-source geo-ontologies","volume":"15","author":"Li","year":"2013","journal-title":"Entropy"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/S0165-0114(98)00402-3","article-title":"Entropy for intuitionistic fuzzy sets","volume":"118","author":"Szmidt","year":"2001","journal-title":"Fuzzy Sets Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s40819-018-0486-x","article-title":"A New Parametric Intuitionistic Fuzzy Entropy and its Applications in Multiple Attribute Decision Making","volume":"4","author":"Joshi","year":"2018","journal-title":"Int. J. Appl. Comput. Math."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.fiae.2016.06.002","article-title":"Distance-based Information Granularity and Hierarchical Structure for an Intuitionistic Fuzzy Granular Space","volume":"8","author":"Huang","year":"2016","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.datak.2012.08.002","article-title":"A completeness analysis of frequent weighted concept lattices and their algebraic properties","volume":"81","author":"Zhang","year":"2012","journal-title":"Data Knowl. Eng."},{"key":"ref_41","first-page":"27","article-title":"Algorithmic Developments of Information Granules of Higher Type and Higher Order and Their Applications","volume":"3","author":"Pedrycz","year":"2016","journal-title":"Fuzzy Log. Soft Comput. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.ins.2018.02.032","article-title":"On interestingness measures of formal concepts","volume":"442","author":"Kuznetsov","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_43","first-page":"96","article-title":"Coverage and invariability in fuzzy systems","volume":"43","year":"2013","journal-title":"Int. J. Gen. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"87","DOI":"10.5391\/IJFIS.2015.15.2.87","article-title":"Concepts and Design Aspects of Granular Models of Type-1 and Type-2","volume":"15","author":"Pedrycz","year":"2015","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10700-009-9052-7","article-title":"Some aspects of intuitionistic fuzzy sets","volume":"8","author":"Yager","year":"2009","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.ins.2019.02.048","article-title":"A temporal-spatial composite sequential approach of three-way granular computing","volume":"486","author":"Yang","year":"2019","journal-title":"Inf. Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/5\/407\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:21:07Z","timestamp":1760124067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/5\/407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,22]]},"references-count":46,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["axioms12050407"],"URL":"https:\/\/doi.org\/10.3390\/axioms12050407","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,22]]}}}