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dc.contributor.authorBorzooei, Rajab Ali
dc.contributor.authorRezaei, Gholam Reza
dc.contributor.authorKologhani, Mona Aaly
dc.contributor.authorJun, Young Bae
dc.description.abstractThe falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.en
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;3en
dc.subjectfuzzy subhoopen
dc.subjectfuzzy filteren
dc.subjectfalling fuzzy subhoopen
dc.subjectfalling fuzzy filteren
dc.titleFalling Shadow Theory with Applications in Hoopsen
dc.contributor.authorAffiliationBorzooei, Rajab Ali - Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematicsen
dc.contributor.authorAffiliationRezaei, Gholam Reza - University of Sistan and Baluchestan, Department of Mathematicsen
dc.contributor.authorAffiliationKologhani, Mona Aaly - Hatef Higher Education Instituteen
dc.contributor.authorAffiliationJun, Young Bae - Gyeongsang National University, Department of Mathematics Educationen
dc.references[1] P. Agliano, I. Ferreirim, F. .Montagna, Basic hoops: An algebraic study of continuous t-norms, Studia Logica, vol. 87 (2007), pp. 73–98, DOI:
dc.references[2] P. Agliano, F. Montagna, Varieties of BL-algebras, I: General properties, Journal of Pure and Applied Algebra, vol. 181(2–3) (2003), pp. 105–129, DOI:
dc.references[3] R. Borzooei, M. A. Kologani, On fuzzy filters of hoop-algebras, The Journal of Fuzzy Mathematics, vol. 25(1) (2017), pp. 177–195.en
dc.references[4] R. A. Borzooei, M. A. Kologani, Filter theory of hoop-algebras, Journal of Advanced Research in Pure Mathematics, vol. 6(4) (2014), pp. 72–86, DOI:
dc.references[5] R. A. Borzooei, M. M. Takallo, M. A. Kologani, Y. B. Jun, Fuzzy sub-hoops based on fuzzy points, submitted.en
dc.references[6] B. Bosbach, Komplementäre halbgruppen. axiomatik und arithmetik, Fundamenta Mathematicae, vol. 64(3) (1969), pp. 257–287.en
dc.references[7] B. Bosbach, Komplementäre Halbgruppen. Kongruenzen und Quotienten, Fundamenta Mathematicae, vol. 69(1) (1970), pp. 1–14.en
dc.references[8] G. Georgescu, L. Leustean, V. Preoteasa, Pseudo-hoops, Journal of Multiple-Valued Logic Soft Computing, vol. 11(1–2) (2005), pp. 153–184.en
dc.references[9] I. Goodman, Fuzzy sets as equivalence classes of random sets, [in:] R. Yager (ed.), Fuzzy Sets and Possibility Theory: Recent Developments, Pergamon, New York (1982), pp. 327–343.en
dc.references[10] Y. Jun, M. Kang, Fuzzifications of generalized Tarski filters in Tarski algebras, Computers and Mathematics with Applications, vol. 61(1) (2011), pp. 1–7, DOI:
dc.references[11] Y. Jun, C. Park, Falling shadows applied to subalgebras and ideals of BCK/BCI-algebras, Honam Mathematical Journal, vol. 34(2) (2012), pp. 135–144, DOI:
dc.references[12] Y. Jun, S. Song, Falling fuzzy quasi-associative ideals of BCI-algebras, Filomat, vol. 26(4) (2012), pp. 649–656, DOI:
dc.references[13] Y. B. Jun, M. S. Kang, Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows, Computers and Mathematics with Applications, vol. 61(1) (2011), pp. 62–67, DOI:
dc.references[14] M. Kondo, Some types of filters in hoops, Multiple-Valued Logic, (ISMVL), (2011), pp. 50–53, DOI:
dc.references[15] S. Tan, P. Wang, E. Lee, Fuzzy set operations based on the theory of falling shadows, Journal of Mathematical Analysis and Applications, vol. 174(1) (1993), pp. 242–255, DOI:
dc.references[16] S. Tan, P. Wang, X. Zhang, Fuzzy inference relation based on the theory of falling shadows, Fuzzy Sets and Systems, vol. 53(2) (1993), pp. 179–188, DOI:
dc.references[17] P. Wang, Fuzzy sets and falling shadows of random sets, Beijing Normal University Press, Beijing, (1985).en
dc.references[18] P. Wang, E. Sanchez, Treating a fuzzy subset as a projectable random set, [in:] M. M. Gupta, E. Sanchez (eds.), Fuzzy Information and Decision, Pergamon, New York (1982), pp. 213-220.en
dc.references[19] X. Yuan, E. Lee, A fuzzy algebraic system based on the theory of falling shadows, Journal of Mathematical Analysis and Applications, vol. 208(1) (1997), pp. 243–251, DOI:
dc.references[20] J. Zhan, Y. Jun, Fuzzy ideals of near-rings based on the theory of falling shadows, UPB Scientific Bulletin, Series A, vol. 74(3) (2012),pp. 67–74.en
dc.references[21] J. Zhan, Y. Jun, H. Kim, Some types of falling fuzzy filters of BL-algebras and its applications, Journal of Intelligent and Fuzzy Systems, vol. 26(4) (2014), pp. 1675–1685, DOI:
dc.contributor.authorEmailBorzooei, Rajab Ali -
dc.contributor.authorEmailRezaei, Gholam Reza -
dc.contributor.authorEmailKologhani, Mona Aaly -
dc.contributor.authorEmailJun, Young Bae -

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