A Note on Multiplicative Fuzzy on BP-Algebras

Authors

  • V. Abisha PG and Research Department of Mathematics, Saiva Bhanu Kshatriya College (affiliated to Madurai Kamaraj University), Madurai, Aruppukottai 626 101, Tamil Nadu, India https://orcid.org/0009-0005-8775-1732
  • N. Kandaraj PG and Research Department of Mathematics, Saiva Bhanu Kshatriya College (affiliated to Madurai Kamaraj University), Madurai, Aruppukottai 626 101, Tamil Nadu, India https://orcid.org/0000-0002-0663-9839
  • V. Thiruveni PG and Research Department of Mathematics, Saiva Bhanu Kshatriya College (affiliated to Madurai Kamaraj University), Madurai, Aruppukottai 626 101, Tamil Nadu, India https://orcid.org/0000-0003-1492-2754

DOI:

https://doi.org/10.26713/cma.v16i2.3249

Keywords:

Absorbing subset, BP-Absorbing subset, Graded set, Multiplicative Fuzzy BP-Algebra

Abstract

Multiplicative fuzzy sets are defined by combining the membership values of the elements in a fuzzy set. This can be considered a generalization of fuzzy sets. Multiplicative fuzzy sets are useful in areas like quantum mechanics. In this paper, we define multiplicative fuzzy BP-algebras using the multiplication operation on membership functions and investigate some of their properties. Multiplicative fuzzy topological BP-algebras are also discussed.

Downloads

Download data is not yet available.

References

V. Abisha and N. Kandaraj, Topology on BP-algebras, Ratio Mathematica 49 (2023), 116 – 126, URL: https://eiris.it/ojs/index.php/ratiomathematica/article/view/116-126/pdf.

M. A. Ahmed and E. A. Ahmed, uzzy BCK-algebras, Journal of Applied Mathematics and Physics 8(5) (2020), 927 – 932, DOI: 10.4236/jamp.2020.85071.

S.-S. Ahn and J.-S. Han, On BP-algebras, Hacettepe Journal of Mathematics and Statistics 42(5) (2013), 551 – 557, URL: https://dergipark.org.tr/tr/download/article-file/86215.

S.-S. Ahn and S.-H. Kwon, Topological properties in BCC-algebras, Communications of the Korean Mathematical Society 23(2) (2008), 169 – 178, DOI: 10.4134/CKMS.2008.23.2.169.

M. Akram and K. H. Dar, On fuzzy d-Algebras, Punjab University Journal of Mathematics 37 (2005), 61 – 76, URL: https://pu.edu.pk/images/jour/akram7.pdf.

M. Annalakshmi and M. Chandramouleeswaran, Fuzzy topological subsystem on a TMalgebra, International Journal of Pure and Applied Mathematics 94(3) (2014), 439 – 449, DOI: 10.12732/ijpam.v94i3.11.

W. A. Dudeck and Y. B. Jun, Fuzzification of ideals in BCC-algebras, Glasnik Matematicki 36(56) (2001), 127 – 138, URL: https://web.math.pmf.unizg.hr/glasnik/36.1/36(1)-12.pdf.

W. A. Dudeck and X. Zhang, On ideals and congruences in BCC-algebras, Czechoslovak Mathematical Journal 48(123) (1998), 21 – 29, DOI: 10.1023/A:1022407325810.

W. A. Dudeck, Y. B. Jun and X. Zhang, On fuzzy topological BCC-algebras, Discussiones Mathematicae - General Algebra and Applications 20(1) (2000), 77 – 86, DOI: 10.7151/dmgaa.1007.

D. H. Foster, Fuzzy topological groups, Journal of Mathematical Analysis and Applications 67(2) (1979), 549 – 564, DOI: 10.1016/0022-247X(79)90043-X.

Y. Imai and K. Iseki, On axiom system of propositional calculi. XIV, Proceedings of the Japan Academy 42 (1966), 19 – 22, URL: https://www.jstage.jst.go.jp/article/pjab1945/42/1/42_1_19/_pdf/-char/ja.

M. Jansi and V. Thiruveni, Complementary role of ideals in TSBF-algebras, Malaya Journal of Matematik 8(3) (2020), 1037 – 1040, URL: https://www.malayajournal.org/articles/MJM08030052.pdf.

D. S. Lee and D. N. Ryu, Notes on topological BCK-algebras, Scientiae Mathematicae 1(2) (1998), 231 – 235, URL: https://www.jams.jp/scm/contents/Vol-1-2/1-2-17.pdf.

K. Megalai and A. Tamilarasi, Fuzzy subalgebras and fuzzy T-ideals in TM-algebras, Journal of Mathematics & Statistics 7(2) (2011), 107 – 111, DOI: 10.3844/jmssp.2011.107.111.

J. Meng, Y. B. Jun and H. S. Kim, Fuzzy implicative ideals of BCK-algebras, Fuzzy Sets and Systems 89(2) (1997), 243 – 248, DOI: 10.1016/S0165-0114(96)00096-6.

Downloads

Published

20-08-2025
CITATION

How to Cite

Abisha, V., Kandaraj, N., & Thiruveni, V. (2025). A Note on Multiplicative Fuzzy on BP-Algebras. Communications in Mathematics and Applications, 16(2), 461–469. https://doi.org/10.26713/cma.v16i2.3249

Issue

Vol. 16 No. 2 (2025)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.