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Fuzzy semi-orthogonality in fuzzy lattices | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 1، 2023، صفحه 78-90 اصل مقاله (280.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2513 | ||
| نویسندگان | ||
| Meenakshi P. Wasadikar1؛ Payal A. Khubchandani* 2 | ||
| 1Formerly of Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India | ||
| 2Department of Engineering Sciences and Humanities, Vishwakarma Institute of Technology, Pune 411037, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fuzzy lattice؛ fuzzy Semi-orthogonality؛ FM-Symmetric؛ ⊥F-symmetric؛ fuzzy modular lattice؛ fuzzy atomic؛ fuzzy atomistic | ||
| مراجع | ||
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[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. | ||
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