{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:51:23Z","timestamp":1761490283377,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,9]],"date-time":"2017-05-09T00:00:00Z","timestamp":1494288000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A similarity measure is a measure evaluating the degree of similarity between two fuzzy data sets and has become an essential tool in many applications including data mining, pattern recognition, and clustering. In this paper, we propose a similarity measure capable of handling non-overlapped data as well as overlapped data and analyze its characteristics on data distributions. We first design the similarity measure based on a distance measure and apply it to overlapped data distributions. From the calculations for example data distributions, we find that, though the similarity calculation is effective, the designed similarity measure cannot distinguish two non-overlapped data distributions, thus resulting in the same value for both data sets. To obtain discriminative similarity values for non-overlapped data, we consider two approaches. The first one is to use a conventional similarity measure after preprocessing non-overlapped data. The second one is to take into account neighbor data information in designing the similarity measure, where we consider the relation to specific data and residual data information. Two artificial patterns of non-overlapped data are analyzed in an illustrative example. The calculation results demonstrate that the proposed similarity measures can discriminate non-overlapped data.<\/jats:p>","DOI":"10.3390\/sym9050068","type":"journal-article","created":{"date-parts":[[2017,5,9]],"date-time":"2017-05-09T11:50:48Z","timestamp":1494330648000},"page":"68","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Analysis of a Similarity Measure for Non-Overlapped Data"],"prefix":"10.3390","volume":"9","author":[{"given":"Sanghyuk","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Xi\u2019an Jiaotong-Liverpool University, Xi\u2019an 215123, China"},{"name":"Centre for Smart Grid and Information Convergence, Xi\u2019an Jiaotong-Liverpool University, Xi\u2019an 215123, China"},{"name":"Biomedical Engineering Centre, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaehoon","family":"Cha","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Xi\u2019an Jiaotong-Liverpool University, Xi\u2019an 215123, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2951-9610","authenticated-orcid":false,"given":"Nipon","family":"Theera-Umpon","sequence":"additional","affiliation":[{"name":"Biomedical Engineering Centre, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Department of Electrical Engineering, Faculty of Engineering Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyeong","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Xi\u2019an Jiaotong-Liverpool University, Xi\u2019an 215123, China"},{"name":"Centre for Smart Grid and Information Convergence, Xi\u2019an Jiaotong-Liverpool University, Xi\u2019an 215123, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,9]]},"reference":[{"key":"ref_1","unstructured":"Zadeh, L.A. Fuzzy sets and systems. Proceedings of the Symposium on System Theory."},{"key":"ref_2","unstructured":"Dubois, D., and Prade, H. (1988). Fuzzy Sets and Systems, Academic Press."},{"key":"ref_3","unstructured":"Kovacic, Z., and Bogdan, S. (2005). Fuzzy Controller Design: Theory and Applications, CRC Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1109\/5.784243","article-title":"Adaptive Fuzzy systems for Multichannel Signal Processing","volume":"87","author":"Plataniotis","year":"1999","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.fss.2016.05.005","article-title":"Fuzzy pattern recognition-based approach to biometric score fusion problem","volume":"305","author":"Fakhar","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_6","first-page":"284","article-title":"Object-background segmentation using new definitions of entropy","volume":"36","author":"Pal","year":"1989","journal-title":"IEEE Proc."},{"key":"ref_7","unstructured":"Kosko, B. (1992). Neural Networks and Fuzzy Systems, Prentice-Hall."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0165-0114(92)90239-Z","article-title":"Entropy, distance measure and similarity measure of fuzzy sets and their relations","volume":"52","author":"Liu","year":"1992","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0020-0255(93)90073-U","article-title":"Some new information measure of fuzzy sets","volume":"67","author":"Bhandari","year":"1993","journal-title":"Inf. Sci."},{"key":"ref_10","first-page":"301","article-title":"A Definition of nonprobabilistic entropy in the setting of fuzzy entropy","volume":"5","author":"Termini","year":"1972","journal-title":"J. Gen. Syst."},{"key":"ref_11","unstructured":"Hsieh, C.H., and Chen, S.H. (1999, January 17\u201320). Similarity of generalized fuzzy numbers with graded mean integration representation. Proceedings of the 8th International Fuzzy Systems Association World Congress, Taipei, Taiwan."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TFUZZ.2002.806316","article-title":"Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers","volume":"11","author":"Chen","year":"2003","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_13","first-page":"67","article-title":"Design of Similarity and Dissimilarity Measures for Fuzzy Sets on the Basis of Distance Measure","volume":"11","author":"Lee","year":"2009","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1587\/transinf.E92.D.1783","article-title":"Study on Entropy and Similarity Measure for Fuzzy Set","volume":"E92-D","author":"Lee","year":"2009","journal-title":"IEICE Trans. Inf. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/978-3-540-85930-7_8","article-title":"Design of Fuzzy Entropy for Non Convex Membership Function","volume":"Volume 15","author":"Lee","year":"2008","journal-title":"Communications in Computer and Information Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0167-8655(01)00110-6","article-title":"New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions","volume":"23","author":"Dengfeng","year":"2002","journal-title":"Pattern Recognit. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.patrec.2006.07.009","article-title":"Similarity measures between intuitionistic fuzzy (vague) set: A comparative analysis","volume":"28","author":"Li","year":"2007","journal-title":"Pattern Recognit. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.ins.2012.11.012","article-title":"Similarity and dissimilarity measures between fuzzy sets: A formal relational study","volume":"229","author":"Couso","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.fss.2013.03.008","article-title":"Some new approaches to constructing similarity measures","volume":"234","author":"Li","year":"2014","journal-title":"Fuzzy Sets Syst."},{"key":"ref_20","unstructured":"Lee, S., Sun, Y., and Wei, H. (2013, January 16\u201318). Analysis on overlapped and non-overlapped data. Proceedings of the Information Technology and Quantitative Management (ITQM2013), Suzhou, China."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lee, S., Wei, H., and Ting, T.O. (2013, January 23\u201325). Study on Similarity Measure for Overlapped and Non-overlapped Data. Proceedings of the Third International Conference on Information Science and Technology, Yangzhou, China.","DOI":"10.1007\/978-94-007-6516-0_33"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1007\/s11771-013-1754-x","article-title":"Similarity measure design on overlapped and non-overlapped data","volume":"20","author":"Lee","year":"2014","journal-title":"J. Cent. South Univ."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Host-Madison, A., and Sabeti, E. (2015, January 14\u201319). Atypical Information Theory for real-vauled data. Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT), Hong Kong, China.","DOI":"10.1109\/ISIT.2015.7282538"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Host-Madison, A., Sabeti, E., and Walton, C. (2013, January 9\u201313). Information Theory for Atypical Sequence. Proceedings of the 2013 IEEE Information Theory Workshop (ITW), Sevilla, Spain.","DOI":"10.1109\/ITW.2013.6691276"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Pemmaraju, S., and Skiena, S. (2003). Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Cambridge University.","DOI":"10.1017\/CBO9781139164849"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/5\/68\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:35:13Z","timestamp":1760207713000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/5\/68"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,9]]},"references-count":25,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5]]}},"alternative-id":["sym9050068"],"URL":"https:\/\/doi.org\/10.3390\/sym9050068","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,5,9]]}}}