Cubic structures applied to ideals of co-residuated lattices

  • Yongwei Yang
Keywords: co-residuated lattice, cubic ideal, Cartesian product

Abstract

The concept of cubic ideals in co-residuated lattices is introduced and some interesting properties are obtained. Characterization theorem of cubic ideals is also discussed by the notion of cubic level sets. We construct Cartesian product of two cubic ideals by using max-min operations, and give some characterizations of them.

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Author Biography

Yongwei Yang

School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

 

References

[1] Chang C C. Algebraic analysis of many valued logics, Transactions of the American Mathematical society, vol. 8, no. 2, pp.
467–490, 1958.
[2] Zheng M C, Wang G J. Co-residuated lattice with application, Fuzzy Systems and Mathematics, vol. 19, no. 4, pp. 1–6, 2005.
[3] Zhu Y Q. On Regular co-residuated lattice and involutory BCK-lattice, Fuzzy Systems and Mathematics, vol. 24, no. 1, pp.
23–28, 2005.
[4] Zheng M C, Wang G J and Liu Y. Ideals and embedding theorem of co-residuated lattices, Journal of Shaanxi Normal University (Natural Science Edition), vol. 34, pp. 1C6, 2006.
[5] Yang Y W, Xin X L, He P F. Characterizations of MV-algebras based on the theory of falling shadows, The Scientific World
Journal, vol. 2014, pp. 1C11, 2014.
[6] Al-Masarwah A, Ahmad A G. Novel concepts of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras[J]. International Journal
of Innovative Computing, Information and Control, vol. 14, no. 6, pp. 2025C2041, 2018.
[7] Liu Y, Zheng M. Characterizations of fuzzy ideals in coresiduated lattices, Advances in Mathematical Physics, vol. 2016, pp.
1C6, 2016.
[8] Jun Y B, Kim, C S, Yang K O. Cubic sets, Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 3, pp. 83–98, 2012.
[9] Jun Y B, LEE K J, Kang M S. Cubic structures applied to ideals of BCI-algebras, Computers & Mathematics with Applications,
vol. 62, no. 9, pp. 3334–3342, 2011.
[10] Senapati T, Shum K P. Cubic implicative ideals of BCK-algebras, Missouri Journal of Mathematical Sciences, vol. 29, no. 2,
pp. 125–138, 2017.
[11] Biswas R. Rosenfeld’s fuzzy subgroups with interval-valued membership functions, Fuzzy sets and systems, vol. 63, no. 1, pp.
87–90, 1994.
Published
2018-11-30
How to Cite
Yang, Y. (2018). Cubic structures applied to ideals of co-residuated lattices. IJRDO -JOURNAL OF MATHEMATICS, 4(11), 01-06. https://doi.org/10.53555/m.v4i11.2568