International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Characteristic Picture Fuzzy Sets and Level Subsets in UP (BCC)-Algebras

  • Pimwaree Kankaew
  • Sunisa Yuphaphin
  • Nattacha Lapo
  • Ronnason Chinram
  • Pongpun Julatha
  • Aiyared Iampan1*
  1. University of Phayao

* Corresponding author

Abstract

The eight new concepts of picture fuzzy sets in UP (BCC)-algebras are introduced by Kankaew et al. in 2022. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP (BCC)-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.

How to Cite

P. Kankaew, S. Yuphaphin, N. Lapo, R. Chinram, P. Julatha, A. Iampan, Characteristic Picture Fuzzy Sets and Level Subsets in UP (BCC)-Algebras, Int. J. Anal. Appl. 21 (2023), 75. https://doi.org/10.28924/2291-8639-21-2023-75

BibTeX
@article{Kankaew2023,
  author  = {Kankaew, Pimwaree and Yuphaphin, Sunisa and Lapo, Nattacha and Chinram, Ronnason and Julatha, Pongpun and Iampan, Aiyared},
  title   = {Characteristic Picture Fuzzy Sets and Level Subsets in UP (BCC)-Algebras},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {75},
  doi     = {10.28924/2291-8639-21-2023-75}
}

References

  • [1] M. Ansari, A. Haidar, A. Koam, On a Graph Associated to UP-Algebras, Math. Comput. Appl. 23 (2018), 61. https://doi.org/10.3390/mca23040061.
  • [2] M.A. Ansari, A.N.A. Koam, A. Haider, Rough set theory applied to UP-algebras, Italian J. Pure Appl. Math. 42 (2019), 388-402.
  • [3] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  • [4] K.T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst. 61 (1994), 137-142.
  • [5] B.C. Cuong, Picture fuzzy sets, J. Computer Sci. Cybern. 30 (2014), 409-420. https://doi.org/10.15625/1813-9663/30/4/5032.
  • [6] B.C. Cuong, V. Kreinovich, Picture fuzzy sets - A new concept for computational intelligence problems, in: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, Hanoi, Vietnam, 2013: pp. 1-6. https://doi.org/10.1109/WICT.2013.7113099.
  • [7] N. Dokkhamdang, A. Kesorn, A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 16 (2018), 171-190. https://doi.org/10.30948/AFMI.2018.16.2.171.
  • [8] A.H. Ganie, S. Singh, P.K. Bhatia, Some new correlation coefficients of picture fuzzy sets with applications, Neural Comput. Appl. 32 (2020), 12609-12625. https://doi.org/10.1007/s00521-020-04715-y.
  • [9] T. Guntasow, S. Sajak, A. Jomkham, et al. Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc. 23 (2017), 1-19.
  • [10] Y. Huang, BCI-algebra, Science Press, Beijing, China, 2006.
  • [11] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Related Topics. 5 (2017), 35-54. https://doi.org/10.22124/jart.2017.2403.
  • [12] A. Iampan, Introducing fully UP-semigroups, Discuss. Math. Gen. Algebra Appl. 38 (2018), 297-306.
  • [13] A. Iampan, Multipliers and near UP-filters of UP-algebras, J. Discr. Math. Sci. Cryptogr. 24 (2019), 667-680. https://doi.org/10.1080/09720529.2019.1649027.
  • [14] A. Iampan, A. Satirad, M. Songsaeng, A note on UP-hyperalgebras, J. Algebr. Hyperstruct. Log. Algebr. 1 (2020), 77-95. https://doi.org/10.29252/hatef.jahla.1.2.7.
  • [15] A. Iampan, M. Songsaeng, G. Muhiuddin, Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math. 13 (2020), 459-471. https://doi.org/10.29020/nybg.ejpam.v13i3.3752.
  • [16] Y. Imai, K. Iséki, On axiom systems of propositional calculi, XIV, Proc. Japan Acad. 4 (1966), 19-22. https://doi.org/10.3792/pja/1195522169.
  • [17] K. Iséki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), 26-29. https://cir.nii.ac.jp/crid/1570009749777934080.
  • [18] Y.B. Jun, B. Brundha, N. Rajesh, et al. (3, 2)-fuzzy UP (BCC)-subalgebras and (3, 2)-fuzzy UP (BCC)-filters, J. Mahani Math. Res. 11 (2022), 1-14. https://doi.org/10.22103/jmmrc.2022.18786.1191.
  • [19] Y.B. Jun, A. Iampan, Comparative and allied UP-filters, Lobachevskii J. Math. 40 (2019), 60-66. https://doi.org/10.1134/s1995080219010086.
  • [20] Y.B. Jun, A. Iampan, Implicative UP-filters, Afr. Mat. 30 (2019), 1093-1101. https://doi.org/10.1007/s13370-019-00704-0.
  • [21] Y.B. Jun, A. Iampan, Shift UP-filters and decompositions of UP-filters in UP-algebras, Missouri J. Math. Sci. 31 (2019), 36-45. https://doi.org/10.35834/mjms/1559181624.
  • [22] P. Kankaew, S. Yuphaphin, N. Lapo, et al. Picture fuzzy set theory applied to UP-algebras, Missouri J. Math. Sci. 34 (2022), 94-120. https://doi.org/10.35834/2022/3401094.
  • [23] H.S. Kim, Y.H. Kim, On BE-algebras, Sci. Math. Japon. 66 (2007), 113-116. https://doi.org/10.32219/isms.66.1_113.
  • [24] Y. Komori, The class of BCC-algebras is not a variety, Math. Japon. 29 (1984), 391-394.
  • [25] P. Mosrijai, A. Iampan, A new branch of bialgebraic structures: UP-bialgebras, J. Taibah Univ. Sci. 13 (2019), 450-459. https://doi.org/10.1080/16583655.2019.1592932.
  • [26] C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna, 5 (2009), 54-57.
  • [27] A. Satirad, R. Chinram, A. Iampan, Four new concepts of extensions of KU/UP-algebras, Missouri J. Math. Sci. 32 (2020), 138-157. https://doi.org/10.35834/2020/3202138.
  • [28] A. Iampan, A. Satirad, Topological UP-Algebras, Discuss. Math. - Gen. Algebra Appl. 39 (2019), 231-250. https://doi.org/10.7151/dmgaa.1317.
  • [29] A. Satirad, P. Mosrijai, A. Iampan, Formulas for Finding UP-Algebras, Int. J. Math. Computer Sci. 14 (2019), 403-409.
  • [30] A. Satirad, P. Mosrijai, A. Iampan, Generalized Power UP-Algebras, Int. J. Math. Computer Sci. 14 (2019), 17-25.
  • [31] T. Senapati, Y.B. Jun, K.P. Shum, Cubic Set Structure Applied in UP-Algebras, Discr. Math. Algorithm. Appl. 10 (2018), 1850049. https://doi.org/10.1142/s1793830918500490.
  • [32] T. Senapati, G. Muhiuddin, K.P. Shum, Representation of UP-Algebras in Interval-Valued Intuitionistic Fuzzy Environment, Italian J. Pure Appl. Math. 38 (2017), 497-517.
  • [33] P. Singh, Correlation Coefficients for Picture Fuzzy Sets, J. Intell. Fuzzy Syst. 28 (2015), 591-604. https://doi.org/10.3233/ifs-141338.
  • [34] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Inform. 12 (2016), 739-756.
  • [35] G. Wei, Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making, Informatica, 28, no. 3, (2017), 547-564.
  • [36] G. Wei, Some Similarity Measures for Picture Fuzzy Sets and Their Applications, Iran. J. Fuzzy Syst. 15 (2018), 77-89.
  • [37] G. Wei, H. Gao, The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications, Informatica, 29 (2018), 107-124.
  • [38] L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338-353. https://doi.org/10.1016/s0019-9958(65)90241-x.