Birkhoff center of Almost Distributive Fuzzy Lattice
Keywords:
Almost distributive fuzzy lattice, almost distributive lattice, Birkhoff center of an almost distributive fuzzy lattice, Birkhoff center of an almost distributive lattice, fuzzy poset, relatively complemented ADFLAbstract
The concept of Birkhoff center B_A(R) of an Almost distributive fuzzy lattice (R,A) with maximal element is introduced. We also prove that BA(R) is relatively complemented ADFL and product of ADFL is a gain ADFL.
References
U. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society (Series A), vol. 31, no. 1, pp. 77–91, 1981.
U. Swamy, G. Rao, R. Kumar, and C. Pragati, “Birkhoff centre of a poset,” Southeast Asian Bulletin of Mathematics, vol. 26, no. 3, pp. 509–516, 2003.
U. Swamy and S. Ramesh, “Birkhoff centre of an almost distributive lattice,” International Journal of Algebra, vol. 3, no. 11, pp. 539–546, 2009.
L. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
J. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.
E. Sanchez, “Resolution of composite fuzzy relation equations,” Information and control, vol. 30, no. 1, pp. 38–48, 1976.
Y. Bo and W. Wangming, “Fuzzy ideals on a distributive lattice,” Fuzzy sets and systems, vol. 35, no. 2, pp. 231–240, 1990.
G. Rao, “Almost distributive lattice,” Ph.D. dissertation, Department of Mathematics, Andhra University, Visakhapatnam, 1980.
I. Chon, “Fuzzy partial order relations and fuzzy lattices,” Korean J. Math, vol. 17, no. 4, pp. 361–374, 2009.
A. Berhanu, G. Yohanes, and T. Bekalu, “Almost distributive fuzzy lattice,” To be communicated.



