{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T04:55:23Z","timestamp":1768712123718,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T00:00:00Z","timestamp":1660176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties.<\/jats:p>","DOI":"10.3390\/axioms11080395","type":"journal-article","created":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T05:43:57Z","timestamp":1660196637000},"page":"395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["General Pseudo Quasi-Overlap Functions on Lattices"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1775-8489","authenticated-orcid":false,"given":"Rui Eduardo Brasileiro","family":"Paiva","sequence":"first","affiliation":[{"name":"Instituto Federal de Educa\u00e7\u00e3o, Ci\u00eancia e Tecnologia do Cear\u00e1, Maracana\u00fa 61939-140, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6757-7934","authenticated-orcid":false,"given":"Benjam\u00edn Ren\u00e9 Callejas","family":"Bedregal","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,11]]},"reference":[{"key":"ref_1","unstructured":"Barros, L., Bassanezi, R., and Lodwick, W. (2016). A First Course in Fuzzy Logic, Fuzzy Dynamical Systems and Biomathematics Theory and Applications, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Massad, E., Ortega, N., de Barros, L., and Struchiner, C. (2009). Fuzzy Logic in Action: Applications in Epidemiology and Beyond, Springer. Studies in Fuzziness and Soft Computing.","DOI":"10.1007\/978-3-540-69094-8"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.asoc.2013.11.009","article-title":"Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system","volume":"20","author":"Sanz","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1016\/j.na.2009.08.033","article-title":"Overlap functions","volume":"72","author":"Bustince","year":"2010","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.ins.2013.05.004","article-title":"New results on overlap and grouping functions","volume":"249","author":"Bedregal","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.fss.2014.04.008","article-title":"Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties","volume":"252","author":"Dimuro","year":"2014","journal-title":"Fuzzy Sets Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.fss.2015.02.008","article-title":"On additive generators of overlap functions","volume":"287","author":"Dimuro","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ijar.2018.11.006","article-title":"The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions","volume":"105","author":"Dimuro","year":"2019","journal-title":"Int. J. Approx. Reason."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.ijar.2019.01.006","article-title":"On binary relations induced from overlap and grouping functions","volume":"106","author":"Qiao","year":"2019","journal-title":"Int. J. Approx. Reason."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.fss.2018.01.007","article-title":"On generalized migrativity property for overlap functions","volume":"357","author":"Qiao","year":"2019","journal-title":"Fuzzy Sets Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.fss.2021.09.005","article-title":"Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions","volume":"441","author":"Asmus","year":"2022","journal-title":"Fuzzy Sets Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1109\/TFUZZ.2021.3052342","article-title":"N-Dimensional Admissibly Ordered Interval-Valued Overlap Functions and Its Influence in Interval-Valued Fuzzy-Rule-Based Classification Systems","volume":"30","author":"Asmus","year":"2022","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_13","first-page":"21","article-title":"The Evolution of the Notion of Overlap Functions","volume":"Volume 394","author":"Bustince","year":"2021","journal-title":"Fuzzy Approaches for Soft Computing and Approximate Reasoning"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.fss.2014.11.023","article-title":"n-Dimensional overlap functions","volume":"287","author":"Montero","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, Z.Q., and Wang, X.P. (2022). The distributivity of extended uninorms over extended overlap functions on the membership functions of type-2 fuzzy sets. Fuzzy Sets Syst., in press.","DOI":"10.1016\/j.fss.2022.04.011"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.engappai.2019.05.016","article-title":"Wavelet-fuzzy power quality diagnosis system with inference method based on overlap functions: Case study in an AC microgrid","volume":"85","author":"Nolasco","year":"2019","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3178","DOI":"10.1109\/TFUZZ.2020.3015594","article-title":"On r\u2192-(Quasi-)Overlap Functions","volume":"29","author":"Qiao","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.fss.2018.08.003","article-title":"General overlap functions","volume":"372","author":"Montero","year":"2019","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, M., Zhang, X., and Bedregal, B. (2022). Constructing general overlap and grouping functions via multiplicative generators. Fuzzy Sets Syst., in press.","DOI":"10.1016\/j.fss.2022.06.011"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.fss.2020.12.018","article-title":"Inflationary BL-algebras obtained from 2-dimensional general overlap functions","volume":"418","author":"Paiva","year":"2021","journal-title":"Fuzzy Sets Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.ijar.2021.04.008","article-title":"Residuated implications derived from quasi-overlap functions on lattices","volume":"134","author":"Paiva","year":"2021","journal-title":"Int. J. Approx. Reason."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ins.2020.03.091","article-title":"General interval-valued overlap functions and interval-valued overlap indices","volume":"527","author":"Asmus","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.ins.2021.02.010","article-title":"Lattice-valued overlap and quasi-overlap functions","volume":"562","author":"Paiva","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijar.2017.07.001","article-title":"Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions","volume":"90","author":"Bedregal","year":"2017","journal-title":"Int. J. Approx. Reason."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.ijar.2020.10.010","article-title":"On interval RO- and (G,O,N)-implications derived from interval overlap and grouping functions","volume":"128","author":"Cao","year":"2021","journal-title":"Int. J. Approx. Reason."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40314-021-01694-1","article-title":"L-valued quasi-overlap functions, L-valued overlap index, and Alexandroff\u2019s topology","volume":"40","author":"Paiva","year":"2021","journal-title":"Comput. Appl. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.ins.2020.06.075","article-title":"Overlap and grouping functions on complete lattices","volume":"542","author":"Qiao","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.fss.2021.03.015","article-title":"Constructing overlap and grouping functions on complete lattices by means of complete homomorphisms","volume":"427","author":"Wang","year":"2022","journal-title":"Fuzzy Sets Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2021.04.019","article-title":"On ordinal sums of overlap and grouping functions on complete lattices","volume":"439","author":"Wang","year":"2022","journal-title":"Fuzzy Sets Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1007\/s40314-021-01694-1","article-title":"General quasi-overlap functions on lattices","volume":"8","author":"Paiva","year":"2021","journal-title":"Proc. Ser. Braz. Soc. Comput. Appl. Math."},{"key":"ref_31","unstructured":"Batista, T. (2022). Generaliza\u00e7\u00f5es da Integral de Choquet como M\u00e9todo de Combina\u00e7\u00e3o em Comit\u00eas de Classificadores. [Ph.D. Thesis, Universidade Federal do Rio Grande do Norte]."},{"key":"ref_32","unstructured":"Zhang, X., and Liang, R. (2022, January 12\u201313). Pseudo overlap functions with applications. Proceedings of the Program of 2022 China-South Korea Non-Classical Logics and Related Algebra Systems Academic Seminar, Online."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhang, X., Liang, R., Bustince, H., Bedregal, B., Fernandez, J., Li, M., and Ou, Q. (2022). Pseudo overlap functions, fuzzy implications and pseudo grouping functions with applications. Fuzzy Sets Syst., manuscript under submision.","DOI":"10.3390\/axioms11110593"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liang, R., and Zhang, X. (2022). Interval-valued pseudo overlap functions and application. Axioms, 11.","DOI":"10.3390\/axioms11050216"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ijar.2021.06.008","article-title":"Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making","volume":"137","author":"Milfont","year":"2021","journal-title":"Int. J. Approx. Reason."},{"key":"ref_36","first-page":"430","article-title":"Revisions to the JDL data fusion model","volume":"Volume 3719","author":"Dasarathy","year":"1999","journal-title":"Sensor Fusion: Architectures, Algorithms, and Applications III"},{"key":"ref_37","unstructured":"Birkhoff, G. (1967). Lattice Theory, American Mathematical Society. [3rd ed.]."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Davey, B.A., and Priestley, H.A. (2002). Introduction to Lattices and Order, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511809088"},{"key":"ref_39","unstructured":"Gr\u00e4tzer, G.A. (2002). General Lattice Theory, Birkh\u00e4user. [2nd ed.]."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Comer, S. (1985). Universal Algebra and Lattice Theory: Proceedings of a Conference Held at Charleston, 11\u201314 July 1984, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/BFb0098450"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/03081079.2017.1291634","article-title":"Aggregation functions on bounded lattices","volume":"46","author":"Mesiar","year":"2017","journal-title":"Int. J. Gen. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3087","DOI":"10.1007\/s00500-019-04642-8","article-title":"General L-fuzzy aggregation functions based on complete residuated lattices","volume":"24","author":"Dan","year":"2020","journal-title":"Soft Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ins.2019.03.077","article-title":"Semi-t-operators on bounded lattices","volume":"490","author":"Fang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Shcherbacov, V. (2017). Elements of Quasigroup Theory and Applications, A Chapman & Hall Book, Taylor & Francis.","DOI":"10.1201\/9781315120058"},{"key":"ref_45","unstructured":"Pflugfelder, H. (1990). Quasigroups and Loops: Introduction, Heldermann. Sigma Series in Pure Mathematics."},{"key":"ref_46","unstructured":"Smith, J. (2009). Introduction to Abstract Algebra, A Chapman & Hall Book, Taylor & Francis."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1090\/S0002-9947-1943-0009962-7","article-title":"Quasigroups. I","volume":"54","author":"Albert","year":"1943","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1090\/S0002-9947-1957-0094404-6","article-title":"On the Foundations of Quasigroups","volume":"85","author":"Stein","year":"1957","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/BF00967815","article-title":"n-ary Quasi-groups and Loops","volume":"7","author":"Belousov","year":"1966","journal-title":"Sib. Math. J."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"7729","DOI":"10.1016\/j.eswa.2012.01.081","article-title":"An alternative to fuzzy methods in decision-making problems","volume":"39","author":"Paternain","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.inffus.2019.10.005","article-title":"The state-of-art of the generalizations of the Choquet integral: From aggregation and pre-aggregation to ordered directionally monotone functions","volume":"57","author":"Dimuro","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.neucom.2022.05.080","article-title":"Constructing multi-layer classifier ensembles using the Choquet integral based on overlap and quasi-overlap functions","volume":"500","author":"Batista","year":"2022","journal-title":"Neurocomputing"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/395\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:07:12Z","timestamp":1760141232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/395"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,11]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["axioms11080395"],"URL":"https:\/\/doi.org\/10.3390\/axioms11080395","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,11]]}}}