{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:33:33Z","timestamp":1760243613827,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T00:00:00Z","timestamp":1383264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Gradual patterns aim at describing co-variations of data such as the higher the size, the higher the weight. In recent years, such patterns have been studied more and more from the data mining point of view. The extraction of such patterns relies on efficient and smart orderings that can be built among data, for instance, when ordering the data with respect to the size, then the data are also ordered with respect to the weight. However, in many application domains, it is hardly possible to consider that data values are crisply ordered. When considering gene expression, it is not true from the biological point of view that Gene 1 is more expressed than Gene 2, if the levels of expression only differ from the tenth decimal. We thus consider fuzzy orderings and fuzzy gamma rank correlation. In this paper, we address two major problems related to this framework: (i) the high memory consumption and (ii) the precision, representation and efficient storage of the fuzzy concordance degrees versus the loss or gain of computing power. For this purpose, we consider multi-precision matrices represented using sparse matrices coupled with parallel algorithms. Experimental results show the interest of our proposal.<\/jats:p>","DOI":"10.3390\/a6040747","type":"journal-article","created":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T12:41:02Z","timestamp":1383309662000},"page":"747-761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multi-Core Parallel Gradual Pattern Mining Based on Multi-Precision Fuzzy Orderings"],"prefix":"10.3390","volume":"6","author":[{"given":"Nicolas","family":"Sicard","sequence":"first","affiliation":[{"name":"Efrei-AllianSTIC, Villejuif 94800, France"}]},{"given":"Yogi","family":"Aryadinata","sequence":"additional","affiliation":[{"name":"LIRMM, University Montpellier 2 - CNRS, Montpellier 34095, France"}]},{"given":"Federico","family":"Del Razo Lopez","sequence":"additional","affiliation":[{"name":"Toluca Institute of Technology, Toluca 64849, Mexico"}]},{"given":"Anne","family":"Laurent","sequence":"additional","affiliation":[{"name":"LIRMM, University Montpellier 2 - CNRS, Montpellier 34095, France"}]},{"given":"Perfecto","family":"Flores","sequence":"additional","affiliation":[{"name":"Apizaco Institute of Technology, Apizaco 90300, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,1]]},"reference":[{"key":"ref_1","unstructured":"Bodenhofer, U. (July, January 30). Fuzzy Orderings of Fuzzy Sets. Proceedings of the 10th IFSA World Congress, Istanbul, Turkey."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/978-3-642-14746-3_47","article-title":"Mining Gradual Dependencies Based on Fuzzy Rank Correlation","volume":"Volume 77","author":"Koh","year":"2010","journal-title":"Combining Soft Computing and Statistical Methods in Data Analysis"},{"key":"ref_3","unstructured":"Lin, N.P., and Chueh, H. (2007, January 15\u201317). Fuzzy Correlation Rules Mining. Proceedings of the 6th WSEAS International Conference on Applied Computer Science, Hangzhou, China."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Laurent, A., Lesot, M.-J., and Rifqi, M. (2009, January 26\u201328). GRAANK: Exploiting Rank Correlations for Extracting Gradual Itemsets. Proceedings of the Eighth International Conference on Flexible Query Answering Systems (FQAS\u201909), Springer, Roskilde, Denmark.","DOI":"10.1007\/978-3-642-04957-6_33"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Quintero, M., Laurent, A., and Poncelet, P. (2011, January 26\u201328). Fuzzy Ordering for Fuzzy Gradual Patterns. Proceedings of the FQAS 2011, Springer, Ghent, Belgium.","DOI":"10.1007\/978-3-642-24764-4_29"},{"key":"ref_6","unstructured":"Di Jorio, L., Laurent, A., and Teisseire, M. (September,, January 31). Mining Frequent Gradual Itemsets from Large Databases. Proceedings of the International Conference on Intelligent Data Analysis (IDA\u201909), Lyon, France."},{"key":"ref_7","unstructured":"Quintero, M., Laurent, A., Poncelet, P., and Sicard, N. (2012, January 10\u201315). Fuzzy Orderings for Fuzzy Gradual Dependencies: Efficient Storage of Concordance Degrees. Proceedings of the FUZZ-IEEE Conference, Brisbane, Australia."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"El-Rewini, H., and Abd-El-Barr, M. (2005). Advanced Computer Architecture Ans Parallel Processing, Wiley.","DOI":"10.1002\/0471478385"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rauber, T., and R\u00fcnger, G. (2010). Parallel Programming: For Multicore and Cluster Systems, Springer.","DOI":"10.1007\/978-3-642-04818-0"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1051\/0004-6361\/200911618","article-title":"Automated supervised classification of variable stars in the CoRoT programme: Method and application to the first four exoplanet fields","volume":"506","author":"Debosscher","year":"2009","journal-title":"Astron. Astrophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1145\/121973.121975","article-title":"What is scalability?","volume":"18","author":"Hill","year":"1990","journal-title":"ACM SIGARCH Comput. Archit. News"},{"key":"ref_12","first-page":"5","article-title":"Roboust rank correlation coefficients on the basis of fuzzy orderings: Initial steps","volume":"15","author":"Bodenhofer","year":"2008","journal-title":"Mathw. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Calders, T., Goethais, B., and Jarszewicz, S. (2006, January 20\u201323). Mining Rank-Correlated Sets of Numerical Attributes. Proceedings of the KDD\u201906.","DOI":"10.1145\/1150402.1150417"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1109\/TC.1972.5009071","article-title":"Some computer organizations and their effectiveness","volume":"C-21","author":"Flynn","year":"1972","journal-title":"IEEE Trans. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"H\u00fcllermeier, E. (2002, January 19\u201323). Association Rules for Expressing Gradual Dependencies. Proceedings of the PKDD Conference, Helsinki, Finland.","DOI":"10.1007\/3-540-45681-3_17"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0020-0255(71)80005-1","article-title":"Similarity relations and fuzzy orderings","volume":"3","author":"Zadeh","year":"1971","journal-title":"Inf. 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