{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T22:39:19Z","timestamp":1775860759862,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,10]],"date-time":"2023-05-10T00:00:00Z","timestamp":1683676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009055","name":"\u00c7anakkale Onsekiz Mart University","doi-asserted-by":"publisher","award":["FHD-2020-3465"],"award-info":[{"award-number":["FHD-2020-3465"]}],"id":[{"id":"10.13039\/100009055","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices), proposed by Engino\u011flu and Arslan in 2020, are worth utilizing in data classification in supervised learning due to coming into prominence with their ability to model decision-making problems. This study aims to define the concepts metrics, quasi-, semi-, and pseudo-metrics and similarities, quasi-, semi-, and pseudo-similarities over ifpifs-matrices; develop a new classifier by using them; and apply it to data classification. To this end, it develops a new classifier, i.e., Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Classifier (IFPIFSC), based on six pseudo-similarities proposed herein. Moreover, this study performs IFPIFSC\u2019s simulations using 20 datasets provided in the UCI Machine Learning Repository and obtains its performance results via five performance metrics, accuracy (Acc), precision (Pre), recall (Rec), macro F-score (MacF), and micro F-score (MicF). It also compares the aforementioned results with those of 10 well-known fuzzy-based classifiers and 5 non-fuzzy-based classifiers. As a result, the mean Acc, Pre, Rec, MacF, and MicF results of IFPIFSC, in comparison with fuzzy-based classifiers, are 94.45%, 88.21%, 86.11%, 87.98%, and 89.62%, the best scores, respectively, and with non-fuzzy-based classifiers, are 94.34%, 88.02%, 85.86%, 87.65%, and 89.44%, the best scores, respectively. Later, this study conducts the statistical evaluations of the performance results using a non-parametric test (Friedman) and a post hoc test (Nemenyi). The critical diagrams of the Nemenyi test manifest the performance differences between the average rankings of IFPIFSC and 10 of the 15 are greater than the critical distance (4.0798). Consequently, IFPIFSC is a convenient method for data classification. Finally, to present opportunities for further research, this study discusses the applications of ifpifs-matrices for machine learning and how to improve IFPIFSC.<\/jats:p>","DOI":"10.3390\/axioms12050463","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T01:37:24Z","timestamp":1683769044000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Distance and Similarity Measures of Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices and Their Applications to Data Classification in Supervised Learning"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0958-5872","authenticated-orcid":false,"given":"Samet","family":"Memi\u015f","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Faculty of Engineering and Natural Sciences, \u0130stanbul Rumeli University, \u0130stanbul 34570, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1724-8841","authenticated-orcid":false,"given":"Burak","family":"Arslan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, \u00c7anakkale Onsekiz Mart University, \u00c7anakkale 17020, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8134-1004","authenticated-orcid":false,"given":"Tu\u011f\u00e7e","family":"Ayd\u0131n","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, \u00c7anakkale Onsekiz Mart University, \u00c7anakkale 17020, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7188-9893","authenticated-orcid":false,"given":"Serdar","family":"Engino\u011flu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, \u00c7anakkale Onsekiz Mart University, \u00c7anakkale 17020, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0122-559X","authenticated-orcid":false,"given":"\u00c7etin","family":"Camc\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, \u00c7anakkale Onsekiz Mart University, \u00c7anakkale 17020, T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,10]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Wu, H.C. (2023). Mathematical Foundations of Fuzzy Sets, Wiley.","DOI":"10.1002\/9781119981558"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory\u2014First results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Comput. Math. Appl."},{"key":"ref_4","unstructured":"Molodtsov, D.A. (2004). Soft Set Theory, URSS. (In Russian)."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/S0898-1221(03)00016-6","article-title":"Soft set theory","volume":"45","author":"Maji","year":"2003","journal-title":"Comput. Math. Appl."},{"key":"ref_6","first-page":"589","article-title":"Fuzzy soft sets","volume":"9","author":"Maji","year":"2001","journal-title":"J. Fuzzy Math."},{"key":"ref_7","first-page":"21","article-title":"Fuzzy parameterized fuzzy soft set theory and its applications","volume":"1","year":"2010","journal-title":"Turk. J. Fuzzy Syst."},{"key":"ref_8","first-page":"1105","article-title":"Fuzzy parameterized fuzzy soft matrices and their application in decision-making","volume":"10","year":"2020","journal-title":"TWMS J. Apl. Eng. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.30516\/bilgesci.643821","article-title":"A data classification method in machine learning based on normalised Hamming pseudo-similarity of fuzzy parameterized fuzzy soft matrices","volume":"3","author":"Erkan","year":"2019","journal-title":"Bilge Int. J. Sci. Technol. Res."},{"key":"ref_10","unstructured":"K\u0131l\u0131\u00e7, M., \u00d6zkan, K., Karaboyac\u0131, M., Ta\u015fdelen, K., Kandemir, H., and Beram, A. (2019, January 26\u201330). An Application of Fuzzy Parameterized Fuzzy Soft Matrices in Data Classification. Proceedings of the International Conferences on Natural Sciences and Technology, Prizren, Kosovo."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"88583","DOI":"10.1109\/ACCESS.2021.3089849","article-title":"Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices","volume":"9","author":"Erkan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Memi\u015f, S., Engino\u011flu, S., and Erkan, U. (2022). A classification method in machine learning based on soft decision-making via fuzzy parameterized fuzzy soft matrices. Soft Comput., 1165\u20131180.","DOI":"10.1007\/s00500-021-06553-z"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"871","DOI":"10.55730\/1300-0632.3816","article-title":"A new classification method using soft decision-making based on an aggregation operator of fuzzy parameterized fuzzy soft matrices","volume":"30","author":"Erkan","year":"2022","journal-title":"Turk. J. Elec. Eng. Comp. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.neucom.2022.05.041","article-title":"Fuzzy parameterized fuzzy soft k-nearest neighbor classifier","volume":"500","author":"Erkan","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Atanassov, K.T. (2012). On Intuitionistic Fuzzy Sets Theory, Springer.","DOI":"10.1007\/978-3-642-29127-2"},{"key":"ref_17","first-page":"677","article-title":"Intuitionistic fuzzy soft sets","volume":"9","author":"Maji","year":"2001","journal-title":"J. Fuzzy Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.asoc.2014.11.053","article-title":"Intuitionistic fuzzy parameterized soft set theory and its decision making","volume":"28","author":"Deli","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_19","first-page":"73","article-title":"Intuitionistic fuzzy parameterised fuzzy soft set","volume":"9","author":"Salleh","year":"2013","journal-title":"J. Qual. Meas. Anal."},{"key":"ref_20","first-page":"607","article-title":"Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making","volume":"11","author":"Karaaslan","year":"2016","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s40314-020-01325-1","article-title":"Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making","volume":"39","author":"Arslan","year":"2020","journal-title":"Comput. Appl. Math."},{"key":"ref_22","first-page":"4","article-title":"UCI Machine Learning Repository","volume":"10","author":"Dua","year":"2019","journal-title":"Intell. Control. Autom."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1109\/TSMC.1985.6313426","article-title":"A fuzzy k-nearest neighbor algorithm","volume":"15","author":"Keller","year":"1985","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_24","first-page":"29","article-title":"FSSC: An algorithm for classifying numerical data using fuzzy soft set theory","volume":"3","author":"Handaga","year":"2012","journal-title":"Int. J. Fuzzy Syst. Appl."},{"key":"ref_25","first-page":"95","article-title":"Medical data classification using similarity measure of fuzzy soft set based distance measure","volume":"9","author":"Lashari","year":"2017","journal-title":"J. Telecommun. Electron. Comput. Eng."},{"key":"ref_26","unstructured":"Ghazali, R., Deris, M.M., Nawi, N.M., and Abawajy, J.H. (2018, January 6\u20137). A Numerical Classification Technique Based on Fuzzy Soft Set using Hamming Distance. Proceedings of the Third International Conference on Soft Computing and Data Mining, Johor, Malaysia."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_28","unstructured":"Breiman, L., Friedman, J.H., Olshen, R.A., and Stone, C.J. (1998). Classification and Regression Trees, CRC Press. [3rd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","article-title":"Greedy function approximation: A gradient boosting machine","volume":"29","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/jcss.1997.1504","article-title":"A decision-theoretic generalization of on-line learning and an application to boosting","volume":"55","author":"Freund","year":"1997","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1214\/aoms\/1177731944","article-title":"A comparison of alternative tests of significance for the problem of m rankings","volume":"11","author":"Friedman","year":"1940","journal-title":"Ann. Math. Stat."},{"key":"ref_33","unstructured":"Nemenyi, P.B. (1963). Distribution-Free Multiple Comparisons, Princeton University."},{"key":"ref_34","first-page":"1","article-title":"Statistical comparisons of classifiers over multiple data sets","volume":"7","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"ref_35","first-page":"59","article-title":"A classification method based on Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices","volume":"10","author":"Arslan","year":"2021","journal-title":"J. New Results Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/j.patrec.2005.10.010","article-title":"An introduction to ROC analysis","volume":"27","author":"Fawcett","year":"2006","journal-title":"Pattern Recognit. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.patcog.2019.06.001","article-title":"Multi-label classification via incremental clustering on an evolving data stream","volume":"95","author":"Nguyen","year":"2019","journal-title":"Pattern Recognit."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5381","DOI":"10.1007\/s00521-020-05343-2","article-title":"A precise and stable machine learning algorithm: Eigenvalue classification (EigenClass)","volume":"33","author":"Erkan","year":"2021","journal-title":"Neural. Comput. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1111\/j.2517-6161.1974.tb00994.x","article-title":"Cross-validatory choice and assessment of statistical predictions","volume":"36","author":"Stone","year":"1974","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_40","unstructured":"Zar, J.H. (2010). Biostatistical Analysis, Prentice Hall. [5th ed.]."},{"key":"ref_41","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. Inf. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Akram, M., and Zafar, F. (2020). Hybrid Soft Computing Models Applied to Graph Theory, Springer International Publishing.","DOI":"10.1007\/978-3-030-16020-3"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1007\/s40314-022-01893-4","article-title":"Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise removal filters","volume":"41","year":"2022","journal-title":"Comput. Appl. Math."},{"key":"ref_44","first-page":"409","article-title":"Picture fuzzy sets","volume":"30","author":"Cuong","year":"2014","journal-title":"J. Comput. Sci. Cybern."},{"key":"ref_45","first-page":"1","article-title":"Another view on picture fuzzy soft sets and their product operations with soft decision-making","volume":"38","year":"2022","journal-title":"J. New Theory"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s12543-013-0127-3","article-title":"New Similarity Measures for Soft Sets and Their Application","volume":"1","author":"Yang","year":"2013","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"15240","DOI":"10.1007\/s40314-022-01837-y","article-title":"Decision-making strategy based on Archimedean Bonferroni mean operators under complex Pythagorean fuzzy information","volume":"41","author":"Garg","year":"2022","journal-title":"Comp. Appl. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s12652-019-01377-0","article-title":"Fermatean fuzzy sets","volume":"11","author":"Senapati","year":"2020","journal-title":"J. Ambient. Intell. Human. Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized orthopair fuzzy sets","volume":"25","author":"Yager","year":"2017","journal-title":"IEEE Trans. Fuzzy. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"106105","DOI":"10.1016\/j.engappai.2023.106105","article-title":"q-rung orthopair fuzzy Aczel\u2013Alsina aggregation operators with multi-criteria decision-making","volume":"122","author":"Farid","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","article-title":"An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets","volume":"31","author":"Mahmood","year":"2019","journal-title":"Neural. Comput. Appl."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.aej.2023.03.053","article-title":"T-spherical fuzzy aggregation operators for dynamic decision-making with its application","volume":"72","author":"Farid","year":"2023","journal-title":"Alex. Eng. J."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2014I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0165-0114(87)90148-5","article-title":"A method of inference in approximate reasoning based on interval-valued fuzzy sets","volume":"21","year":"1987","journal-title":"Fuzzy Sets Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","article-title":"Interval valued intuitionistic fuzzy sets","volume":"31","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"ref_56","unstructured":"Zhang, W.R. (1994, January 18\u201321). Bipolar Fuzzy Sets and Relations: A Computational Framework for Cognitive Modeling and Multiagent Decision Analysis. Proceedings of the NAFIPS\/IFIS\/NASA \u201994 First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, The Industrial Fuzzy Control and Intelligent Systems, San Antonio, CA, USA."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"4690808","DOI":"10.1155\/2020\/4690808","article-title":"A novel approach toward bipolar soft sets and their applications","volume":"2020","author":"Mahmood","year":"2020","journal-title":"J. Math."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/s13370-019-00738-4","article-title":"Bipolar FPSS-tsheory with applications in decision making","volume":"31","author":"Deli","year":"2020","journal-title":"Afr. Mat."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Fix, E., and Hodges, J.L. (1951). Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties, USAF School of Aviation Medicine, Randolph Field.","DOI":"10.1037\/e471672008-001"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TIT.1967.1053964","article-title":"Nearest Neighbor Pattern Classification","volume":"13","author":"Cover","year":"1967","journal-title":"IEEE Trans. Inf."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/5\/463\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:32:33Z","timestamp":1760124753000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/5\/463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,10]]},"references-count":60,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["axioms12050463"],"URL":"https:\/\/doi.org\/10.3390\/axioms12050463","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,10]]}}}