General quasi-overlap functions on lattices
DOI:
https://doi.org/10.5540/03.2021.008.01.0417Palavras-chave:
Aggregation functions, General quasi-overlap functions, LatticesResumo
One recent work, Paivaet al. introduced the concept of quasi-overlap functions onbounded lattices and investigated some vital properties of them. In this paper, we continue considerthis research topic and focus on a generalization, called general quasi-overlap functions, whichmeasure the degree of overlapping of several classes in a given classification system and for anygiven object. We also provide a characterization, as well as some methods of constructing thesefunctions.Downloads
Referências
De Barros, L. C., Bassanezi, R. and Lodwick, W.A First Course in Fuzzy Logic, FuzzyDynamical Systems and Biomathematics Theory and Applications. InStudies in Fuzzinessand Soft Computing. Springer, 2017. ISSN 1434-9922.[2] Bedregal, B., Bustince, H., Palmeira, E., Dimuro, G. and Fernandez, J.Generalizedinterval-valued OWA operators with interval weights derived from interval-valued over-lap functions,International Journal of Approximate Reasoning, 90:1–16, 2017. DOI:10.1016/j.ijar.2017.07.001.[3] Birkhoff, G.Lattice Theory, 3rd edition. American Mathematical Society, Providence, 1967.[4] Da Cruz, A. T., Dimuro, G. P., Bedregal, B., Sanz, J. A., Pereira, S. and Bustince, H. Generalinterval-valued overlap functions and interval-valued overlap indices,Information Sciences,527:27–50, 2020. DOI: 10.1016/j.ins.2020.03.091.
[5] Dan, Y., Hu, B. and Qiao, J. General L-fuzzy aggregation functions based on completeresiduated lattices,Soft Comput, 24:3087–3112, 2020. DOI: 10.1007/s00500-019-04642-8.[6] Davey, B. A. and Priestley, H. A.Introduction to Lattices and Order, 2rd edition. CambridgeUniversity Press, Cambridge, 2002.[7] De Miguel, L., G ́omez, D., Rodr ́ıguez, J. T., Montero, J., Bustince, H., Dimuro, G. P. andSanz, J. A. General overlap functions,Fuzzy Sets and Systems, 372:81–96, 2018. DOI:10.1016/j.fss.2018.08.003.[8] Dimuro, G. P., Bedregal, B., Bustince, H., Asi ́ain, M. J. and Mesiar, R. On additive generatorsof overlap functions,Fuzzy Sets and Systems, 287:76–96, 2016. DOI: 10.1016/j.fss.2015.02.008.[9] Dimuro, G. P., Fern ́andez, J., Bedregal, B., Mesiar, R., Sanz, J. A., Lucca, G. and Bustince,H. The state-of-art of the generalizations of the Choquet integral: From aggregation andpre-aggregation to ordered directionally monotone functions,Information Fusion, 57:27–43,2020. DOI: 10.1016/j.inffus.2019.10.005.[10] G ́omez, D., Rodr ́ıguez, J. T., Montero, J., Bustince, H. and Barrenechea, E. n-dimensionaloverlap functions,Fuzzy Sets and Systems, 287:57 – 75, 2016. DOI: 10.1016/j.fss.2014.11.023.[11] Kara ̧cal, F. and Mesiar, R. Aggregation functions on bounded lattices,International Journalof General Systems, 46:37–51, 2017. DOI: 10.1080/03081079.2017.1291634.[12] Massad, E., Ortega, N., de Barros, L. and Struchiner, C. Fuzzy Logic in Action: Applicationsin Epidemiology and Beyond. InStudies in Fuzziness and Soft Computing. Springer BerlinHeidelberg, 2009. ISSN: 1434-9922.[13] Paiva, R., Santiago, R., Bedregal, B. and Rivieccio, U. Inflationary BL-algebras obtainedfrom 2-dimensional general overlap functions,Fuzzy Sets and Systems, 418:64–83, 2021. DOI:10.1016/j.fss.2020.12.018.[14] Paiva, R., Santiago, R., Bedregal, B. and Palmeira, E. Lattice-valued overlap and quasi-overlap functions,Information Sciences, 562:180–199, 2021. DOI: 10.1016/j.ins.2021.02.010.[15] Paiva, R., Bedregal, B., Santiago, R. and Vieira, T. Residuated implications derived fromquasi-overlap functions on lattices,International Journal of Approximate Reasoning, 134:95–110, 2021. DOI: 10.1016/j.ijar.2021.04.008.[16] Pflugfelder, H. Quasigroups and loops: introduction. InSigma series in pure mathematics.Heldermann Verlag, 1990. ISSN: 0936-8272.[17] Sanz, J. A., Galar, M., Jurio, A., Brugos, A., Pagola, M. and Bustince, H. Medical diagnosis ofcardiovascular diseases using an interval-valued fuzzy rule-based classification system,AppliedSoft Computing, 20:103–111, 2014. DOI: 10.1016/j.asoc.2013.11.009.[18] Shcherbacov, V.Elements of Quasigroup Theory and Applications.InChapman andHall/CRC Monographs and Research Notes in Mathematics Series. Taylor & Francis, 2017.ISSN: 2372-9309.[19] Smith, J.Introduction to Abstract Algebra (Textbooks in Mathematics), 1rd edition. Taylor &Francis, Ames 2008.
