Fuzzy semi-orthogonality in fuzzy lattices

Document Type : Research Paper

Authors

1 Formerly of Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India

2 Department of Engineering Sciences and Humanities, Vishwakarma Institute of Technology, Pune 411037, India

Abstract

We consider the notion of fuzzy lattices introduced by Chon and define a fuzzy semi-ortholattice and a fuzzy
semi-orthocomplemented lattice. We investigate some algebraic proper-ties of these fuzzy lattices such as a sufficient condition of a fuzzy semi-lattice and the equivalent relationship between fuzzy covering property and fuzzy exchange property in fuzzy lattices.

Keywords


[1] F. Maeda and S. Maeda, Theory of Symmetric Lattices, Springer-verlag, Berlin,1970.
[2] I. Chon, Fuzzy partial order relations and fuzzy lattices, Korean J. Math., 17(4) (2009), 361–374.
[3] I. Mezzomo, B. Bedregal and R. Santiago, Kinds of ideals of fuzzy lattices, Second Brazilian Congress on Fuzzy Systems, (2012), 657–671.
[4] I. Mezzomo, B. Bedregal and R. Santiago, On fuzzy ideals of fuzzy lattices, IEEE International Conference on Fuzzy Systems, (2012), 1–5.doi: 10.1109/FUZZ-IEEE.2012.6251307.
[5] I. Mezzomo, B. Bedregal and R. Santiago, Operations on bounded fuzzy lattices, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), (2013), 151–156. doi:10.1109/IFSA-NAFIPS.2013.6608391
[6] L. Wilcox, Modularity in the theory of lattices, Annals of Mathematics, 40(2)(1939), 490–505.
[7] L. Wilcox, A note on complementation in lattices, Bull. Amer. Math. Soc., 48(1942), 453–458.
[8] L. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338–353.
[9] L. Zadeh, Similarity relations and fuzzy orderings Information Sciences, 3 (1971),177–200.
[10] M. P. Wasadikar and P. A. Khubchandani, Fuzzy modularity in fuzzy lattices,The Journal of Fuzzy Mathematics,
27(4) (2019), 985–998.
[11] M. P. Wasadikar and P. A. Khubchandani, Fuzzy modularity and complement in fuzzy lattices, TWMS J. App. and Eng. Math., 12(4) (2022), 1368–1379.
[12] N. Ajmal and K. V. Thomas, Fuzzy lattices, Information Sciences, 79 (1994),271–291.