Fuzzy Amicable sets of an Almost Distributive Fuzzy Lattice
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Abstract
In this paper, we introduce the concept of Fuzzy Amicable sets, we prove some properties of Fuzzy Amicable set, too. We also prove that two Fuzzy compatible elements of an Almost distributive Fuzzy Lattice (ADFL) are equal if and only if their corresponding unique Fuzzy amicable elements are equal. We define the homomorphism of two Almost Distributive Fuzzy lattices (ADFL) and finally we observe that any two Fuzzy amicable set in an Almost Distributive Fuzzy Lattice (ADFL) are isomorphic.
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References
U. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society (Series A), vol. 31, no. 01, pp. 77–91, 1981.
L. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
E. Sanchez, “Resolution of composite fuzzy relation equations,” Information and control, vol. 30, no. 1, pp. 38–48, 1976.
J. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.
Y. Bo and W. Wangming, “Fuzzy ideals on a distributive lattice,” Fuzzy sets and systems, vol. 35, no. 2, pp. 231–240, 1990.
N. Ajmal and K. Thomas, “Fuzzy lattices,” Information sciences, vol. 79, no. 3-4, pp. 271–291, 1994.
M. Atallah, “Completely fuzzy prime ideals of distributive lattices,” Journal of Fuzzy Mathematics, vol. 8, no. 1, pp. 151–156, 2000.
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,” Submitted.