Picture fuzzy sets in UP-algebras by means of a special type

Volume 25, Issue 1, pp 37--72 http://dx.doi.org/10.22436/jmcs.025.01.05

Publication Date: May 04, 2021 Submission Date: March 14, 2021 Revision Date: April 02, 2021 Accteptance Date: April 07, 2021

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1490 Downloads
• 3189 Views

Authors

Sunisa Yuphaphin - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Pimwaree Kankaew - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Nattacha Lapo - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Ronnason Chinram - Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Aiyared Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand.

Abstract

The concept of picture fuzzy sets was first introduced by Cuong and Kreinovich [B. C. Cuong, V. Kreinovich, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, (2013), 1--6] in 2013, which is direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. In this paper, we applied the concept of picture fuzzy sets in UP-algebras to introduce the eight new concepts of picture fuzzy sets by means of a special type: special picture fuzzy UP-subalgebras, special picture fuzzy near UP-filters, special picture fuzzy UP-filters, special picture fuzzy implicative UP-filters, special picture fuzzy comparative UP-filters, special picture fuzzy shift UP-filters, special picture fuzzy UP-ideals, and special picture fuzzy strong UP-ideals. Also, we discuss the relationship between the eight new concepts of picture fuzzy sets in UP-algebras. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.

Share and Cite

Keywords

• UP-algebra
• picture fuzzy set
• special picture fuzzy UP-subalgebra
• special picture fuzzy near UP-filter
• special picture fuzzy UP-filter
• special picture fuzzy implicative UP-filter
• special picture fuzzy shift UP-filter
• special picture fuzzy UP-ideal
• special picture fuzzy strong UP-ideal

MSC

•  06F35
•  08A72
•  03E72

References

• [1] M. A. Ansari, A. Haidar, A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl., 23 (2018), 12 pages
  • View Article


• [2] M. A. Ansari, A. N. A. Koam, A. Haider, Rough set theory applied to UP-algebras, Ital. J. Pure Appl. Math., 42 (2019), 388--402
  • View Article


• [3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96
  • View Article


• [4] K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61 (1994), 137--142
  • View Article


• [5] B. C. Cuong, Picture fuzzy sets, J. Comput. Sci. Cybernet., 30 (2014), 409--420
  • View Article


• [6] B. C. Cuong, V. Kreinovich, Picture fuzzy sets-a new concept for computational intelligence problems, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, 2013 (2013), 1--6
  • View Article


• [7] N. Dokkhamdang, A. Kesorn, A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 16 (2018), 171--190
  • View Article


• [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
  • View Article


• [9] T. Guntasow, S. Sajak, A. Jomkham, A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc, 23 (2017), 1--19
  • View Article


• [10] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Topics, 5 (2017), 35--54
  • View Article


• [11] A. Iampan, Introducing fully UP-semigroups, Discuss. Math. Gen. Algebra Appl., 38 (2018), 297--306
  • View Article


• [12] A. Iampan, Multipliers and near UP-filters of UP-algebras, J. Discrete Math. Sci. Cryptogr., 2019 (2019), 1--14
  • View Article


• [13] A. Iampan, A. Satirad, M. Songsaeng, A note on UP-hyperalgebras, J. Algebr. Hyperstruct. Log. Algebr., 1 (2020), 77--95
  • View Article


• [14] A. Iampan, M. Songsaeng, G. Muhiuddin, Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math., 13 (2020), 459--471
  • View Article


• [15] Y. Imai, K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42 (1966), 19--22
  • View Article


• [16] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26--29
  • View Article


• [17] H. S. Kim, Y. H. Kim, On BE-algebras, Sci. Math. Jpn., 66 (2007), 113--116
  • View Article


• [18] C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna, 5 (2009), 54--57
  • View Article


• [19] A. Satirad, R. Chinram, A. Iampan, Four new concepts of extensions of KU/UP-algebras, Missouri J. Math. Sci., 32 (2020), 138--157
  • View Article


• [20] A. Satirad, A. Iampan, Topological UP-algebras, Discuss. Math. Gen. Algebra Appl., 39 (2019), 231--250
  • View Article


• [21] A. Satirad, P. Mosrijai, A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 403--409
  • View Article


• [22] A. Satirad, P. Mosrijai, A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 17--25
  • View Article


• [23] T. Senapati, Y. B. Jun, K. P. Shum, Cubic set structure applied in UP-algebras, Discrete Math. Algorithms Appl., 10 (2018), 23 pages
  • View Article


• [24] T. Senapati, G. Muhiuddin, K. P. Shum, Representation of UP-algebras in interval-valued intuitionistic fuzzy environment, Ital. J. Pure Appl. Math., 38 (2017), 497--517
  • View Article


• [25] P. Singh, Correlation coefficients for picture fuzzy sets, J. Intell. Fuzzy Systems, 28 (2015), 591--604
  • View Article


• [26] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12 (2016), 739--756
  • View Article


• [27] G. Wei, Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making, Informatica, 28 (2017), 547--564
  • View Article


• [28] G. Wei, Some similarity measures for picture fuzzy sets and their applcations, Iran. J. Fuzzy Syst., 15 (2018), 77--89
  • View Article


• [29] G. Wei, H. Gao, The generalized Dice similarity measures for picture fuzzy sets and their applications, Informatica, 29 (2018), 107--124
  • View Article


• [30] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338--353
  • View Article