N-FOLD GENERALIZED HESITANT IMPLICATIVE FILTERS OF HOOPS
DOI:
https://doi.org/10.53555/eijms.v5i1.28Abstract
To investigate implicative filters of hoops furthermore, we apply n-fold theory to (α, β)-hesitant fuzzy implicative filters and introduce the notion of n-fold (α,β)-hesitant fuzzy implicative filters, and obtain some conditions for a (α,β)-hesitant fuzzy filter to be a n-fold (α,β)-hesitant fuzzy implicative filter. We also study the preimage and image of n-fold (α, β)-hesitant fuzzy implicative filters.
References
. B. Bosbach, Komplementare halbgruppen. axiomatik und arithmetik, Fundamenta Mathematicae 64(3) (1969)
–287.¨
. Y. Yang, L. Lu, Q. Wang, Pseudo valuation on hoop-algebra respect to filters, International Journal of Mathematics
and Statistics 2(11) (2017) 12–19.
. Y. Yang, n-fold implicative pseudo valuations on hoops, IJRDO-Journal of Mathematics 4(10) (2018) 1–5.
. M. Wang, X. Xin, J. Wang, Implicative pseudo valuations on hoops, Chinese Quarterly Journal of Mathematics
(1) (2018 51–60.
. M. Kondo, Some types of filters in hoops, International Symposium on Multiple-Valued Logic 47 (2011) 50–53.
. S.Z. Alavi, R.A. Borzooei, M A. Kologani, Filter theory of pseudo hoop-algebras, Italian Journal of Pure & Applied
Mathematics 37 (2017) 619–632.
. C. Luo, X. Xin, P. He, n-fold (positive) implicative filters of hoops, Italian Journal of Pure & Applied Mathematics
(2017) 631–642.
. V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6) (2010) 529–539.
. Y.B. Jun, S.A. Sun, Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Mathematical Journal
(4) (2014) 813–830.
. Y.B. Jun, S.A. Sun, Hesitant fuzzy set theory applied to BCK/BCI-algebras, Journal of Computational Analysis &
Applications 20(4) (2016) 635-646.
. Y. Yang, L. Lu, Q. Liu, Characterizations of hoop-algebras via generalized hesitant fuzzy filters, Global Journal
of Mathematics 11(2) (2017) 475–750.
. Y. Yang. (M, N)-hesitant fuzzy implicative filters of hoops, IOSR Journal of Mathematics 14(5) (2018) 7–12.
. R.T. Khorami, A.B. Saeid, Some unitary operators on hoop-algebras, Fuzzy Information and Engineering 9(2)
(2017) 205–223.
. R.A. Borzooei, H.R. Varasteh, K. Borna, Fundamental hoop-algebras, Ratio Mathematica 29 (2015) 25–40
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