B-almost distributive fuzzy lattice

Berhanu Assaye; Mihret Alemneh; Gerima Tefera

Bulletin of the Section of Logic (2018)

  • Volume: 47, Issue: 3
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Berhanu Assaye, Mihret Alemneh, and Gerima Tefera. "B-almost distributive fuzzy lattice." Bulletin of the Section of Logic 47.3 (2018): null. <http://eudml.org/doc/295510>.

@article{BerhanuAssaye2018,
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.},
author = {Berhanu Assaye, Mihret Alemneh, Gerima Tefera},
journal = {Bulletin of the Section of Logic},
keywords = {almost distributive lattice; Heyting almost distributive lattice (HADL); B-almost distributive lattice; principal ideals of an almost distributive lattice},
language = {eng},
number = {3},
pages = {null},
title = {B-almost distributive fuzzy lattice},
url = {http://eudml.org/doc/295510},
volume = {47},
year = {2018},
}

TY - JOUR
AU - Berhanu Assaye
AU - Mihret Alemneh
AU - Gerima Tefera
TI - B-almost distributive fuzzy lattice
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 3
SP - null
AB - 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.
LA - eng
KW - almost distributive lattice; Heyting almost distributive lattice (HADL); B-almost distributive lattice; principal ideals of an almost distributive lattice
UR - http://eudml.org/doc/295510
ER -

References

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  1. 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. 
  2. G. Epstein and A. Horn, P-algebras, an abstraction from Post algebras, Algebra Universalis 4(1) (1974), pp. 195–206. 
  3. Inheung Chon, Fuzzy partial order Relations and Fuzzy Lattices, Korean Journal of Mathematics 17 (2009), No. 4, pp. 361–374. 
  4. I. Mezzemo, B. C. Bedregas, R. H. N. Santiago, Kinds of fuzzy lattices, second Brazilian Congress on Fuzzy System 2012, pp. 657–671. 
  5. G. C. Rao, A. Berhanu, M. V. Ratnamani, Heyting Almost Distributive Lattices, International Journal of Computational Cognition 8(3) (2000), pp. 131–138. 
  6. G. C. Rao, Naveen Kumar Kakuman, B-Almost Distributive Lattice, Southeast Asian Bulletin of Mathematics 39 (2015), pp. 545–554. 
  7. G. C. Rao, Almost Distributive Lattice, Doctorial thesis, Department of Mathematics, Andra University, Visakhapatnam, 1980. 
  8. U. M. Swammy and S. Ramesh, Birkhoff center of Almost Distributive Lattices, International Journal of Algebra 3 (2009), pp. 539–546. 
  9. U. M. Swammy and G. C. Rao, Almost Distributive Lattices, Journal of the Australian Mathematical Society (Ser A) 31 (1981), pp. 77–91. 
  10. 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. 

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