1. bookVolume 42 (2022): Issue 1 (March 2022)
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
access type Open Access

Fuzzy Distributive Pairs in Fuzzy Lattices

Published Online: 05 Apr 2022
Volume & Issue: Volume 42 (2022) - Issue 1 (March 2022)
Page range: 179 - 199
Received: 30 Jan 2020
Accepted: 25 Dec 2020
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
Abstract

We generalize the concept of a fuzzy distributive lattice by introducing the concepts of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair in a fuzzy lattice. A relationship among a fuzzy join-distributive pair, a fuzzy join-semidistributive pair and a fuzzy join-modular pair is proved. It is shown that for a pair of fuzzy atoms, the notions of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair coincide.

Keywords

MSC 2010

[1] N. Ajmal and K.V. Thomas, Fuzzy lattices, Information Sci. 79 (1994) 271–291. https://doi.org/10.1016/0020-0255(94)90124-410.1016/0020-0255(94)90124-4 Search in Google Scholar

[2] I. Chon, Fuzzy partial order relations and fuzzy lattices, Korean J. Math. 17 (4) (2009) 361–374. Search in Google Scholar

[3] G. Gratzer, Lattice Theory Foundations, Springer Verlag, berlin, 2011. https://doi.org/10.1007/978-3-0348-0018-110.1007/978-3-0348-0018-1 Search in Google Scholar

[4] S. Maeda, On distributive pairs in lattices, Acta Math. Acad. Sci. Hung. 45 (1985) 133–140. https://doi.org/10.1007/BF0195503010.1007/BF01955030 Search in Google Scholar

[5] F. Maeda and S. Maeda, Theory of Symmetric Lattices (Springer-Verlag, Berlin, 1970). https://doi.org/10.1007/978-3-642-46248-110.1007/978-3-642-46248-1 Search in Google Scholar

[6] I. Mezzomo, B. Bedregal and R. Santiago, On fuzzy ideals of fuzzy lattices, 2012 IEEE International Conference on Fuzzy Systems, Brisbane, QLD, 2012, 1–5. https://doi.org/10.1109/FUZZ-IEEE.2012.625130710.1109/FUZZ-IEEE.2012.6251307 Search in Google Scholar

[7] I. Mezzomo, B. Bedregal and R. Santiago, Operations on bounded fuzzy lattices, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS) – 2013 Joint, 151–156. https://doi.org/10.1109/IFSA-NAFIPS.2013.660839110.1109/IFSA-NAFIPS.2013.6608391 Search in Google Scholar

[8] I. Mezzomo, B. Bedregal and R. Santiago, Types of fuzzy ideals in fuzzy lattices, J. Intelligent and Fuzzy Systems 28 (2) (2015) 929–945. https://doi.org/10.3233/IFS-14137410.3233/IFS-141374 Search in Google Scholar

[9] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512–517. https://doi.org/10.1016/0022-247X(71)90199-510.1016/0022-247X(71)90199-5 Search in Google Scholar

[10] N.K. Thakare, M.P. Wasadikar and S. Maeda, On modular pairs in semilattices, Alg. Univ. 19 (1984) 255–265. https://doi.org/10.1007/BF0119043510.1007/BF01190435 Search in Google Scholar

[11] M. Wasadikar and P. Khubchandani, Fuzzy modularity in fuzzy lattices, J. Fuzzy Math. 27 (4) (2019) 985–998. Search in Google Scholar

[12] B. Yaun and W. Wu, Fuzzy ideals on distributive lattices, Fuzzy Sets and Systems 35 (1990) 231–240. https://doi.org/10.1016/0165-0114(90)90196-D10.1016/0165-0114(90)90196-D Search in Google Scholar

[13] L. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X10.1016/S0019-9958(65)90241-X Search in Google Scholar

[14] L. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971) 177–200. https://doi.org/10.1016/S0020-0255(71)80005-110.1016/S0020-0255(71)80005-1 Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo