{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T04:43:36Z","timestamp":1725857016288},"publisher-location":"Cham","reference-count":47,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319393834"},{"type":"electronic","value":"9783319393841"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-39384-1_10","type":"book-chapter","created":{"date-parts":[[2016,5,28]],"date-time":"2016-05-28T03:40:39Z","timestamp":1464406839000},"page":"114-124","source":"Crossref","is-referenced-by-count":12,"title":["A Modification of the Silhouette Index for the Improvement of Cluster Validity Assessment"],"prefix":"10.1007","author":[{"given":"Artur","family":"Starczewski","sequence":"first","affiliation":[]},{"given":"Adam","family":"Krzy\u017cak","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,5,29]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1016\/j.eswa.2012.05.049","volume":"40","author":"MB Baskir","year":"2013","unstructured":"Baskir, M.B., T\u00fcrksen, I.B.: Enhanced fuzzy clustering algorithm and cluster validity index for human perception. Expert Syst. Appl. 40, 929\u2013937 (2013)","journal-title":"Expert Syst. Appl."},{"issue":"1","key":"10_CR2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1515\/jaiscr-2016-0001","volume":"6","author":"E Bas","year":"2016","unstructured":"Bas, E.: The training of multiplicative neuron model based artificial neural networks with differential evolution algorithm for forecasting. J. Artif. Intell. Soft Comput. Res. 6(1), 5\u201311 (2016)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"2","key":"10_CR3","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1515\/jaiscr-2016-0010","volume":"6","author":"JR Bertini","year":"2016","unstructured":"Bertini, J.R., Nicoletti, M.C.: Enhancing constructive neural network performance using functionally expanded input data. J. Artif. Intell. Soft Comput. Res. 6(2), 119\u2013131 (2016)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"9","key":"10_CR4","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1109\/TPDS.2014.2357019","volume":"26","author":"J Bilski","year":"2015","unstructured":"Bilski, J., Smolag, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561\u20132570 (2015)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"10_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/978-3-319-07173-2_2","volume-title":"Artificial Intelligence and Soft Computing","author":"J Bilski","year":"2014","unstructured":"Bilski, J., Smol\u0105g, J., Galushkin, A.I.: The parallel approach to the conjugate gradient learning algorithm for the feedforward neural networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 12\u201321. Springer, Heidelberg (2014)"},{"key":"10_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/978-3-642-38658-9_3","volume-title":"Artificial Intelligence and Soft Computing","author":"J Bilski","year":"2013","unstructured":"Bilski, J., Smol\u0105g, J.: Parallel approach to learning of the recurrent jordan neural network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 32\u201340. Springer, Heidelberg (2013)"},{"key":"10_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/978-3-642-29347-4_2","volume-title":"Artificial Intelligence and Soft Computing","author":"J Bilski","year":"2012","unstructured":"Bilski, J., Smolag, J.: Parallel Realisation of the Recurrent Multi Layer Perceptron Learning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 12\u201320. Springer, Heidelberg (2012)"},{"key":"10_CR8","doi-asserted-by":"crossref","unstructured":"Cpalka, K., Rutkowski, L.: Flexible Takagi-Sugeno fuzzy systems. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN), vols 1-5 Book Series: IEEE International Joint Conference on Neural Networks, pp. 1764\u20131769 (2005)","DOI":"10.1109\/IJCNN.2005.1556147"},{"issue":"6","key":"10_CR9","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1080\/03081079.2013.798912","volume":"42","author":"K Cpaka","year":"2013","unstructured":"Cpaka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. Gen Syst 42(6), 706\u2013720 (2013)","journal-title":"Int. J. Gen Syst"},{"key":"10_CR10","unstructured":"Duch, W., Korbicz, J., Rutkowski, L., Tadeusiewicz, R. (eds.): Biocybernetics and biomedical engineering 2000. Neural Networks, vol. 6, Akademicka Oficyna Wydawnicza, EXIT, (2000)"},{"issue":"9","key":"10_CR11","doi-asserted-by":"crossref","first-page":"3034","DOI":"10.1016\/j.patcog.2014.03.017","volume":"47","author":"P Fr\u00e4nti","year":"2014","unstructured":"Fr\u00e4nti, P., Rezaei, M., Zhao, Q.: Centroid index: cluster level similarity measure. Pattern Recognit. 47(9), 3034\u20133045 (2014)","journal-title":"Pattern Recognit."},{"issue":"8","key":"10_CR12","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/TPAMI.2003.1217600","volume":"25","author":"LN Fred","year":"2003","unstructured":"Fred, L.N., Leitao, M.N.: A new cluster isolation criterion based on dissimilarity increments. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 944\u2013958 (2003)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10_CR13","volume-title":"Algorithms for Clustering Data","author":"A Jain","year":"1988","unstructured":"Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)"},{"issue":"15","key":"10_CR14","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1016\/j.patrec.2005.04.007","volume":"26","author":"M Kim","year":"2005","unstructured":"Kim, M., Ramakrishna, R.S.: New indices for cluster validity assessment. Pattern Recogn. Lett. 26(15), 2353\u20132363 (2005)","journal-title":"Pattern Recogn. Lett."},{"key":"10_CR15","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.ins.2015.08.030","volume":"327","author":"M Korytkowski","year":"2016","unstructured":"Korytkowski, M., Rutkowski, L., Scherer, R.: Fast image classification by boosting fuzzy classifiers. Inf. Sci. 327, 175\u2013182 (2016)","journal-title":"Inf. Sci."},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/978-3-540-69731-2_26","volume-title":"Artificial Intelligence and Soft Computing \u2013 ICAISC 2008","author":"M Korytkowski","year":"2008","unstructured":"Korytkowski, M., Rutkowski, L., Scherer, R.: From ensemble of fuzzy classifiers to single fuzzy rule base classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265\u2013272. Springer, Heidelberg (2008)"},{"issue":"3","key":"10_CR17","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1515\/jaiscr-2015-0006","volume":"4","author":"AS Koshiyama","year":"2014","unstructured":"Koshiyama, A.S., Vellasco, M., Tanscheit, R.: GPFIS-Control: a genetic fuzzy system for control tasks. J. Artif. Intell. Soft Comput. Res. 4(3), 167\u2013179 (2014)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"4","key":"10_CR18","doi-asserted-by":"crossref","first-page":"457","DOI":"10.3233\/FI-2015-1221","volume":"138","author":"L Laskowski","year":"2015","unstructured":"Laskowski, L., Jelonkiewicz, J.: Self-correcting neural network for stereo-matching problem solving. Fundamenta Informaticae 138(4), 457\u2013482 (2015)","journal-title":"Fundamenta Informaticae"},{"issue":"5","key":"10_CR19","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1142\/S0129065710002498","volume":"20","author":"X Li","year":"2010","unstructured":"Li, X., Er, M.J., Lim, B.S., et al.: Fuzzy regression modeling for tool performance prediction and degradation detection. Int. J. Neural Syst. 20(5), 405\u2013419 (2010)","journal-title":"Int. J. Neural Syst."},{"key":"10_CR20","volume-title":"UCI Machine Learning Repository","author":"M Lichman","year":"2013","unstructured":"Lichman, M.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine (2013). http:\/\/archive.ics.uci.edu\/ml"},{"issue":"4","key":"10_CR21","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1515\/jaiscr-2015-0035","volume":"5","author":"H Miyajima","year":"2015","unstructured":"Miyajima, H., Shigei, N., Miyajima, H.: Performance comparison of hybrid electromagnetism-like mechanism algorithms with descent method. J. Artif. Intell. Soft Comput. Res. 5(4), 271\u2013282 (2015)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"1","key":"10_CR22","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2011.07.036","volume":"184","author":"I Ozkan","year":"2012","unstructured":"Ozkan, I., T\u00fcrksen, I.B.: MiniMax $$\\varepsilon $$ \u03b5 -stable cluster validity index for Type-2 fuzziness. Inf. Sci. 184(1), 64\u201374 (2012)","journal-title":"Inf. Sci."},{"issue":"3","key":"10_CR23","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/91.413225","volume":"3","author":"NR Pal","year":"1995","unstructured":"Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3(3), 370\u2013379 (1995)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"1","key":"10_CR24","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1515\/jaiscr-2015-0019","volume":"5","author":"C Patgiri","year":"2015","unstructured":"Patgiri, C., Sarma, M., Sarma, K.K.: A class of neuro-computational methods for assamese fricative classification. J. Artif. Intell. Soft Comput. Res. 5(1), 59\u201370 (2015)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"4","key":"10_CR25","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1515\/jaiscr-2015-0011","volume":"4","author":"G Rigatos","year":"2014","unstructured":"Rigatos, G., Siano, P.: Flatness-based adaptive fuzzy control of spark-ignited engines. J. Artif. Intell. Soft Comput. Res. 4(4), 231\u2013242 (2014)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"3","key":"10_CR26","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/TNN.2003.811698","volume":"14","author":"L Rutkowski","year":"2003","unstructured":"Rutkowski, L., Cpalka, K.: Flexible neuro-fuzzy systems. IEEE Trans. Neural Networks 14(3), 554\u2013574 (2003)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"2","key":"10_CR27","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/TIE.2011.2161652","volume":"59","author":"L Rutkowski","year":"2012","unstructured":"Rutkowski, L., Przybyl, A., Cpalka, K.: Novel online speed profile generation for industrial machine tool based on flexible neuro-fuzzy approximation. IEEE Trans. Industr. Electron. 59(2), 1238\u20131247 (2012)","journal-title":"IEEE Trans. Industr. Electron."},{"issue":"1","key":"10_CR28","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TFUZZ.2004.836069","volume":"13","author":"L Rutkowski","year":"2005","unstructured":"Rutkowski, L., Cpalka, K.: Designing and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems. IEEE Trans. Fuzzy Syst. 13(1), 140\u2013151 (2005)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Rutkowski, L., Cpalka, K.: A general approach to neuro-fuzzy systems. In: 10th IEEE International Conference on Fuzzy Systems, vols. 1\u20133: Meeting the Grand Challenge: Machines that Serve People, pp. 1428\u20131431 (2001)","DOI":"10.1109\/FUZZ.2001.1008927"},{"issue":"2","key":"10_CR30","first-page":"297","volume":"31","author":"L Rutkowski","year":"2002","unstructured":"Rutkowski, L., Cpalka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control Cybern. 31(2), 297\u2013308 (2002)","journal-title":"Control Cybern."},{"key":"10_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1007\/978-3-642-13232-2_79","volume-title":"Artifical Intelligence and Soft Computing","author":"L Rutkowski","year":"2010","unstructured":"Rutkowski, L., Przyby\u0142, A., Cpa\u0142ka, K., Er, M.J.: Online Speed Profile Generation for Industrial Machine Tool Based on Neuro-fuzzy Approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS, vol. 6114, pp. 645\u2013650. Springer, Heidelberg (2010)"},{"key":"10_CR32","first-page":"85","volume":"76","author":"L Rutkowski","year":"2002","unstructured":"Rutkowski, L., Cpalka, K.: Compromise approach to neuro-fuzzy systems. Technol. Book Ser. Frontiers Artif. Intell. Appl. 76, 85\u201390 (2002)","journal-title":"Technol. Book Ser. Frontiers Artif. Intell. Appl."},{"issue":"6","key":"10_CR33","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1109\/TKDE.2012.66","volume":"25","author":"L Rutkowski","year":"2013","unstructured":"Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the McDiarmids bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272\u20131279 (2013)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"1","key":"10_CR34","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/TKDE.2013.34","volume":"26","author":"L Rutkowski","year":"2014","unstructured":"Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the Gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108\u2013119 (2014)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"5","key":"10_CR35","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1109\/TNNLS.2014.2333557","volume":"26","author":"L Rutkowski","year":"2015","unstructured":"Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Networks Learn. Syst. 26(5), 1048\u20131059 (2015)","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"10_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2013.12.060","volume":"266","author":"L Rutkowski","year":"2014","unstructured":"Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Inf. Sci. 266, 1\u201315 (2014)","journal-title":"Inf. Sci."},{"issue":"1","key":"10_CR37","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1515\/jaiscr-2015-0020","volume":"5","author":"D Saitoh","year":"2015","unstructured":"Saitoh, D., Hara, K.: Mutual learning using nonlinear perceptron. J. Artif. Intell. Soft Comput. Res. 5(1), 71\u201377 (2015)","journal-title":"J. Artif. Intell. Soft Comput. Res."},{"issue":"1","key":"10_CR38","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s10044-007-0099-1","volume":"12","author":"AS Sameh","year":"2009","unstructured":"Sameh, A.S., Asoke, K.N.: Development of assessment criteria for clustering algorithms. Pattern Anal. Appl. 12(1), 79\u201398 (2009)","journal-title":"Pattern Anal. Appl."},{"key":"10_CR39","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.asoc.2014.05.001","volume":"22","author":"H-L Shieh","year":"2014","unstructured":"Shieh, H.-L.: Robust validity index for a modified subtractive clustering algorithm. Appl. Soft Comput. 22, 47\u201359 (2014)","journal-title":"Appl. Soft Comput."},{"key":"10_CR40","doi-asserted-by":"crossref","unstructured":"Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. (2015). doi: 10.1007\/s10044-015-0525-8","DOI":"10.1007\/s10044-015-0525-8"},{"key":"10_CR41","series-title":"Advances in Soft Computing","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1007\/978-3-7908-1902-1_87","volume-title":"Neural Networks and Soft Computing","author":"J Starczewski","year":"2003","unstructured":"Starczewski, J., Rutkowski, L.: Interval type 2 neuro-fuzzy systems based on interval consequents. In: Rutkowski, L., Kacprzyk, J. (eds.) Neural Networks and Soft Computing. Advances in Soft Computing, pp. 570\u2013577. Springer-Verlag, Physica-Verlag HD, Heidelberg (2003)"},{"key":"10_CR42","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1007\/3-540-48086-2_70","volume-title":"Parallel Processing and Applied Mathematics","author":"JT Starczewski","year":"2002","unstructured":"Starczewski, J.T., Rutkowski, L.: Connectionist structures of type 2 fuzzy inference systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Wa\u015bniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, p. 634. Springer, Heidelberg (2002)"},{"key":"10_CR43","unstructured":"Weka 3: Data mining software in Java. University of Waikato, New Zealand. http:\/\/www.cs.waikato.ac.nz\/ml\/weka"},{"key":"10_CR44","doi-asserted-by":"crossref","unstructured":"Wozniak, M., Polap, D., Nowicki, R., Napoli, C., Pappalardo, G., Tramontana, E.: Novel approach toward medical signals classifier. In: 2015 International Joint Conference on Neural Networks (IJCNN), Killarney, Irlandia (2015). doi: 10.1109\/IJCNN.2015.7280556","DOI":"10.1109\/IJCNN.2015.7280556"},{"key":"10_CR45","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1016\/j.patcog.2009.02.010","volume":"42","author":"KL Wu","year":"2009","unstructured":"Wu, K.L., Yang, M.S., Hsieh, J.N.: Robust cluster validity indexes. Pattern Recogn. 42, 2541\u20132550 (2009)","journal-title":"Pattern Recogn."},{"key":"10_CR46","doi-asserted-by":"crossref","first-page":"3374","DOI":"10.1016\/j.patcog.2010.04.025","volume":"43","author":"KR Zalik","year":"2010","unstructured":"Zalik, K.R.: Cluster validity index for estimation of fuzzy clusters of different sizes and densities. Pattern Recogn. 43, 3374\u20133390 (2010)","journal-title":"Pattern Recogn."},{"key":"10_CR47","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.fss.2013.12.013","volume":"253","author":"D Zhang","year":"2014","unstructured":"Zhang, D., Ji, M., Yang, J., Zhang, Y., Xie, F.: A novel cluster validity index for fuzzy clustering based on bipartite modularity. Fuzzy Sets Syst. 253, 122\u2013137 (2014)","journal-title":"Fuzzy Sets Syst."}],"container-title":["Lecture Notes in Computer Science","Artificial Intelligence and Soft Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-39384-1_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,8]],"date-time":"2019-09-08T20:42:13Z","timestamp":1567975333000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-39384-1_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319393834","9783319393841"],"references-count":47,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-39384-1_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}