Show simple item record

Constructing a Hoop Using Rough Filters

dc.contributor.authorBorzooei, Rajab Ali
dc.contributor.authorBabaei, Elham
dc.date.accessioned2022-11-07T14:09:17Z
dc.date.available2022-11-07T14:09:17Z
dc.date.issued2022-09-09
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/44039
dc.description.abstractWhen it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;3en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjecthoopen
dc.subjectrough seten
dc.subjectrough approximations (lower and upper)en
dc.subjectrough filteren
dc.titleConstructing a Hoop Using Rough Filtersen
dc.typeOther
dc.page.number363-382
dc.contributor.authorAffiliationBorzooei, Rajab Ali - Shahid Beheshti University, Department of Mathematics, Faculty of Mathematical Sciences, Tehran 1983963113, Iranen
dc.contributor.authorAffiliationBabaei, Elham - Shahid Beheshti University, Department of Mathematics, Faculty of Mathematical Sciences, Tehran 1983963113, Iranen
dc.identifier.eissn2449-836X
dc.referencesM. Aaly Kologani, R. A. Borzooei, On ideal theory of hoops, Mathematica Bohemica, vol. 145(2) (2020), pp. 141–162, DOI: https://doi.org/10.21136/MB.2019.0140-17en
dc.referencesM. Aaly Kologani, S. Z. Song, R. A. Borzooei, Y. B. Jun, Constructing some logical algebras with hoops, Mathematics, vol. 7 (2019), p. 1243, DOI: https://doi.org/10.3390/math7121243en
dc.referencesP. Aglianò, I. M. A. Ferreirim, F. Montagna, Basic hoops: An algebraic study of continuous t-norms, Studia Logica, vol. 87 (2007), pp. 73–98, DOI: https://doi.org/10.1007/s11225-007-9078-1en
dc.referencesR. Biswas, S. Nanda, Rough groups and rough subgroups, Bulletin of the Polish Academy of Sciences. Mathematics, vol. 42(3) (1994), pp. 251–254.en
dc.referencesR. A. Borzooei, M. Aaly Kologani, Results on hoops, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 1(1) (2020), pp. 61–77, DOI: https://doi.org/10.29252/HATEF.JAHLA.1.1.5en
dc.referencesR. A. Borzooei, E. Babaei, Y. B. J. nad M. Aaly Kologani, M. Mohseni Takallo, Soft set theory applied to hoops, Analele Universitatii Ovidius Constanta-Seria Matematica, vol. 28(1) (2020), pp. 61–79, DOI: https://doi.org/10.2478/auom-2020-0004en
dc.referencesR. A. Borzooei, M. Sabetkish, E. H. Roh, M. Aaly Kologani, Int-soft filters in hoops, International Journal of Fuzzy Logic and Intelligent Systems, vol. 19(3) (2019), pp. 213–222, DOI: https://doi.org/10.5391/IJFIS.2019.19.3.213en
dc.referencesB. Bosbach, Komplementäre Halbgruppen. Kongruenzen and Quotienten, Fundamenta Mathematicae, vol. 69(1) (1970), pp. 1–14, URL: http://matwbn.icm.edu.pl/ksiazki/fm/fm69/fm6911.pdfen
dc.referencesG. Georgescu, L. Leustean, V. Preoteasa, Pseudo-hoops, Journal of Multiple-Valued Logic and Soft Computing, vol. 11(1–2) (2005), pp. 153–184, URL: http://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-11-number-1-2-2005/mvlsc-11-1-2-p-153-184/en
dc.referencesP. Hájek, Metamathematics of Fuzzy Logic, Springer, vol. 4 (1998), DOI: https://doi.org/10.1007/978-94-011-5300-3en
dc.referencesT. B. Iwiński, Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences, vol. 42(3) (1994), pp. 251–254.en
dc.referencesI. M. James, Introduction to Uniform Spaces, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (2013), DOI: https://doi.org/10.1017/CBO9780511721519en
dc.referencesY. B. Jun, Roughness of ideals in BCK-algebras, Scientiae Mathematicae Japonicae Online, vol. 7 (2002), pp. 115–119, URL: https://www.jams.jp/scm/contents/Vol-7-2/7-13.pdfen
dc.referencesY. B. Jun, K. H. Kim, Rough set theory applied to BCC-algebras, International Mathematical Forum, vol. 2(41–44) (2007), pp. 2023–2029.en
dc.referencesN. Kuroki, Rough ideals in semigroups, Information Sciences, vol. 100(1–4) (1997), pp. 139–163, DOI: https://doi.org/10.1016/S0020-0255(96)00274-5en
dc.referencesN. Kuroki, J. Mordeson, Structure of rough sets and rough groups, Journal of Fuzzy Mathematics, vol. 5 (1997), pp. 183–191.en
dc.referencesR. Rasoul, B. Davvaz, Roughness in MV-Algebra, Information Siences, vol. 180(5) (2010), pp. 737–747, DOI: https://doi.org/10.1016/j.ins.2009.11.008en
dc.contributor.authorEmailBorzooei, Rajab Ali - borzooei@sbu.ac.ir
dc.contributor.authorEmailBabaei, Elham - Elhambabaei64@gmail.com
dc.identifier.doi10.18778/0138-0680.2022.10
dc.relation.volume51


Files in this item

Thumbnail
Name:
363-382_Borzooei,_Babaei.pdf
Size:
1.749Mb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record

https://creativecommons.org/licenses/by-nc-nd/4.0
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0