B-almost distributive fuzzy lattice

Authors

  • Berhanu Assaye Ethiopia, Bahir Dar, Bahir Dar University, College of Science, Department of Mathematics
  • Mihret Alemneh Ethiopia, Bahir Dar, Bahir Dar University, College of Science, Department of Mathematics
  • Gerima Tefera Dessie, Ethiopia, Wollo University, College of Natural Science, Department of Mathematics

DOI:

https://doi.org/10.18778/0138-0680.47.3.03

Keywords:

almost distributive lattice, Heyting almost distributive lattice (HADL), B-almost distributive lattice, principal ideals of an almost distributive lattice

Abstract

The paper introduces the concept of B-Almost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also prove the equivalency of B-algebra and B-fuzzy algebra. In addition, we extend PSADL to PSADFL and prove that B-ADFL implies PSADFL.

References

A. Berhanu, G. Yohannes and T. Bekalu, Almost Distributive Fuzzy Lattice, International Journal of Mathematics and its application, Vol. 5, Isue 1C (2017), pp. 307–316.
Google Scholar

G. Epstein and A. Horn, P-algebras, an abstraction from Post algebras, Algebra Universalis 4(1) (1974), pp. 195–206.
Google Scholar

Inheung Chon, Fuzzy partial order Relations and Fuzzy Lattices, Korean Journal of Mathematics 17 (2009), No. 4, pp. 361–374.
Google Scholar

I. Mezzemo, B. C. Bedregas, R. H. N. Santiago, Kinds of fuzzy lattices, second Brazilian Congress on Fuzzy System 2012, pp. 657–671.
Google Scholar

G. C. Rao, A. Berhanu, M. V. Ratnamani, Heyting Almost Distributive Lattices, International Journal of Computational Cognition 8(3) (2000), pp. 131–138.
Google Scholar

G. C. Rao, Naveen Kumar Kakuman, B-Almost Distributive Lattice, Southeast Asian Bulletin of Mathematics 39 (2015), pp. 545–554.
Google Scholar

G. C. Rao, Almost Distributive Lattice, Doctorial thesis, Department of Mathematics, Andra University, Visakhapatnam, 1980.
Google Scholar

U. M. Swammy and S. Ramesh, Birkhoff center of Almost Distributive Lattices, International Journal of Algebra 3 (2009), pp. 539–546.
Google Scholar

U. M. Swammy and G. C. Rao, Almost Distributive Lattices, Journal of the Australian Mathematical Society (Ser A) 31 (1981), pp. 77–91.
Google Scholar

U. M. Swamy, G. C. Rap and G. N. Rao, Pseudo-Complementation on Almost Distributive Lattices, Southeast Asian Bulletin of Mathematics 24 (2000), pp. 95–104.
Google Scholar

Downloads

Published

2018-10-30

How to Cite

Assaye, B., Alemneh, M., & Tefera, G. (2018). B-almost distributive fuzzy lattice. Bulletin of the Section of Logic, 47(3), 171–185. https://doi.org/10.18778/0138-0680.47.3.03

Issue

Vol. 47 No. 3 (2018)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC