Heyting Almost Distributive fuzzy Lattices

Berhanu Assaye Alaba, Derebew Nigussie Derso

Abstract


In this paper, we introduce the concept of Heyting almost distributive fuzzy lattices (HADFL) using the concepts of Heyting almost distributive lattices (HADL), almost distributive fuzzy lattices, fuzzy partial order relation and fuzzy Heyting algebra. Using the properties of fuzzy Heyting algebra, we also give a necessary and sufficient condition for an HADFL to be fuzzy Heyting algebra (FHA).

Keywords


Heyting Almost distributive fuzzy Lattices; Almost distributive fuzzy lattices; Fuzzy Heyting algebra; fuzzy partial order relations

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References


U. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society, vol. 31, no. 1, pp. 77–91, 1981.

G. Rao, B. Assaye, and M. Mani, “Heyting almost distributive lattices,” Inter. J. Computational Cognition, vol. 8, no. 3, pp. 85–89, 2010.

L. Zadeh, “Information and control,” Fuzzy sets, vol. 8, no. 3, pp. 338–353, 1965.

I. Mezzomo, “On fuzzy ideals and fuzzy filters of fuzzy lattices,” Ph.D. dissertation, Universidade Federal do Rio Grande do Norte, Dec. 2013.

B. Alaba and D. Derso, Fuzzy Heyting Algebra. Springer, Cham, 2018, pp. 25–33.

R. Balbes and A. Horn, “Injective and projective heyting algebras,” Transactions of the American Mathematical Society, vol. 148, no. 2, pp. 549–559, 1970.

I. Chon, “Fuzzy partial order relations and fuzzy lattices,” Korean J. Math, vol. 17, no. 4, pp. 361–374, 2009.

B. Assaye, Y. Gedamu, and B. Tarekegn, “Almost distributive fuzzy lattices,” International Journal of Mathematics and Its Applications, vol. 5, no. 1-C, pp. 307–316, 2017.




DOI: http://dx.doi.org/10.12962/j24775401.v4i1.3000

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International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.