Journal of applied mathematics & informatics

  • 제41권3호
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  • Pages.657-685
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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PYTHAGOREAN FUZZY SOFT SETS OVER UP-ALGEBRAS

  • AKARACHAI SATIRAD (Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao) ;
  • RUKCHART PRASERTPONG (Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University) ;
  • PONGPUN JULATHA (Faculty of Science and Technology, Pibulsongkram Rajabhat University) ;
  • RONNASON CHINRAM (Division of Computational Science, Faculty of Science, Prince of Songkla University) ;
  • AIYARED IAMPAN (Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao)
  • 투고 : 2022.11.13
  • 심사 : 2022.12.20
  • 발행 : 2023.05.30
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초록

This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss t-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.

키워드

과제정보

This work was supported by the revenue budget in 2022, School of Science, University of Phayao, Thailand (Grant No. PBTSC65020).

참고문헌

  1. M.A. Ansari, A. Haidar, and A.N.A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl. 23 (2018), Article number: 61.
  2. M.A. Ansari, A.N.A. Koam, and A. Haider, Rough set theory applied to UP-algebras, Ital. 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. N. Dokkhamdang, A. Kesorn, and 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
  5. T. Guntasow, S. Sajak, A. Jomkham, and A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc. 23 (2017), 1-19.
  6. A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5 (2017), 35-54.
  7. A. Iampan, Introducing fully UP-semigroups, Discuss. Math., Gen. Algebra Appl. 38 (2018), 297-306. https://doi.org/10.7151/dmgaa.1290
  8. A. Iampan, Multipliers and near UP-filters of UP-algebras, J. Discrete Math. Sci. Cryptography 24 (2021), 667-680. https://doi.org/10.1080/09720529.2019.1649027
  9. A. Iampan, M. Songsaeng, and G. Muhiuddin, Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math. 13 (2020), 459-471.
  10. C. Jana, H. Garg, and M. Pal, Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method, J. Ambient Intell. Human. Comput. (2022), in press.
  11. C. Jana and M. Pal, Application of bipolar intuitionistic fuzzy soft sets in decision making problem, Int. J. Fuzzy Syst. Appl. 7 (2018), 32-55.
  12. C. Jana and M. Pal, Extended bipolar fuzzy EDAS approach for multi-criteria group decision-making process, Comput. Appl. Math. 40 (2021), Article number: 9.
  13. C. Jana, T. Senapati, and M. Pal, Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures, IGI Global, USA, 2019.
  14. C. Jana, T. Senapati, and M. Pal, Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making, Int. J. Intell. Syst. 34 (2019), 2019-2038. https://doi.org/10.1002/int.22125
  15. C. Jana, T. Senapati, K.P. Shum, and M. Pal, Bipolar fuzzy soft subalgebras and ideals of BCK/BCI-algebras based on bipolar fuzzy points, J. Intell. Fuzzy Syst. 37 (2019), 2785-2795. https://doi.org/10.3233/JIFS-18877
  16. P.K. Maji, R. Biswas, and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (2001), 589-602.
  17. D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  18. P. Mosrijai and 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
  19. M. Palanikumar, K. Arulmozhi, and C. Jana, Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators, Comput. Appl. Math. 41 (2022), Article number: 90.
  20. X. Peng, Y. Yang, J. Song, and Y. Jiang, Pythagorean fuzzy soft set and its application, Comput. Eng. 41 (2015), 224-229.
  21. C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna. 5 (2009), 54-57.
  22. A. Rehman, S. Abdullah, M. Aslam, and M.S. Kamran, A study on fuzzy soft set and its operations, Ann. Fuzzy Math. Inform. 6 (2013), 339-362.
  23. A. Satirad, R. Chinram, and A. Iampan, Pythagorean fuzzy sets in UP-algebras and approximations, AIMS Math. 6 (2021), 6002-6032. https://doi.org/10.3934/math.2021354
  24. A. Satirad, R. Chinram, P. Julatha, and A. Iampan, New types of rough Pythagorean fuzzy UP-filters of UP-algebras, J. Math. Comput. Sci. 28 (2022), 236-257. https://doi.org/10.22436/jmcs.028.03.03
  25. A. Satirad, R. Chinram, P. Julatha, and A. Iampan, Rough Pythagorean fuzzy sets in UP-algebras, Eur. J. Pure Appl. Math. 15 (2022), 169-198. https://doi.org/10.29020/nybg.ejpam.v15i1.4254
  26. A. Satirad and A. Iampan, Fuzzy sets in fully UP-semigroups, Ital. J. Pure Appl. Math. 42 (2019), 539-558. https://doi.org/10.29020/nybg.ejpam.v12i2.3412
  27. A. Satirad and A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math. 12 (2019), 294-331. https://doi.org/10.29020/nybg.ejpam.v12i2.3412
  28. A. Satirad and A. Iampan, Properties of operations for fuzzy soft sets over fully UP-semigroups, Int. J. Anal. Appl. 17 (2019), 821-837.
  29. A. Satirad and A. Iampan, Topological UP-algebras, Discuss. Math., Gen. Algebra Appl. 39 (2019), 231-250. https://doi.org/10.7151/dmgaa.1317
  30. A. Satirad, P. Mosrijai, and A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci. 14 (2019), 403-409.
  31. A. Satirad, P. Mosrijai, and A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci. 14 (2019), 17-25.
  32. A. Satirad, P. Mosrijai, W. Kamti, and A. Iampan, Level subsets of a hesitant fuzzy set on UP-algebras, Ann. Fuzzy Math. Inform. 14 (2017), 279-302. https://doi.org/10.30948/afmi.2017.14.3.279
  33. T. Senapati, Y.B. Jun, and K.P. Shum, Cubic set structure applied in UP-algebras, Discrete Math. Algorithms Appl. 10 (2018), 1850049.
  34. T. Senapati, G. Muhiuddin, and K.P. Shum, Representation of UP-algebras in interval-valued intuitionistic fuzzy environment, Ital. J. Pure Appl. Math. 38 (2017), 497-517.
  35. T. Senapati and R.R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Human. Comput. 11 (2020), 663-674. https://doi.org/10.1007/s12652-019-01377-0
  36. J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12 (2016), 739-756.
  37. V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529-539.
  38. V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, 18th IEEE Int. Conf. Fuzzy Syst. (2009), 1378-1382.
  39. M. Touqeer, Intuitionistic fuzzy soft set theoretic approaches to α-ideals in BCI-algebras, Fuzzy inf. Eng. 12 (2020), 150-180. https://doi.org/10.1080/16168658.2020.1751405
  40. R.R. Yager, Pythagorean fuzzy subsets, 2013 Jt. IFSA World Congr. NAFIPS Annu. Meet. (IFSA/NAFIPS), Edmomton, Canada, 2013, 57-61.
  41. R.R. Yager and A.M. Abbasov, Pythagorean member grades, complex numbers, and decision making, Int. J. Intell. Syst. 28 (2013), 436-452. https://doi.org/10.1002/int.21584
  42. L.A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X