Acknowledgement
Supported by : University of Phayao
The authors would also like to thank the anonymous referee for giving many helpful suggestion on the revision of present paper.
References
- M. A. Ansari, A. Haidar, and A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl. 23 (4) (2018), 61. https://doi.org/10.3390/mca23040061
- 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.
- K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
- K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst. 61 (1994), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
- M. Bhowmik, T. Senapati, and M. Pal, Intuitionistic L-fuzzy ideals of BG-algebras, Afr. Mat. 25 (2014), 577-590. https://doi.org/10.1007/s13370-013-0139-5
- N. Dokkhamdang, A. Kesorn, and A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 16 (2) (2018), 171-190. https://doi.org/10.30948/afmi.2018.16.2.171
- T. Guntasow, S. Sajak, A. Jomkham, and A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc. 23 (2) (2017), 1-19. https://doi.org/10.22342/jims.23.2.371.1-19
- A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5 (1) (2017), 35-54.
- A. Iampan, Introducing fully UP-semigroups, Discuss. Math., Gen. Algebra Appl. 38 (2) (2018), 297-306. https://doi.org/10.7151/dmgaa.1290
- A. Iampan, Multipliers and near UP-filters of UP-algebras, Manuscript accepted for publication in J. Discrete Math. Sci. Cryptography, July 2019.
- C. Jana, T. Senapati, M. Bhowmik, and M. Pal, On intuitionistic fuzzy G-subalgebras of G-algebras, Fuzzy Inf. Eng. 7 (2) (2015), 195-209. https://doi.org/10.1016/j.fiae.2015.05.005
- Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideal of BCK-algebras, Internat. J. Math. & Math. Sci. 24 (12) (2000), 839-849. https://doi.org/10.1155/S0161171200004610
- B. Kesorn, K. Maimun, W. Ratbandan, and A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math. 34 (2015), 339-364.
- K. H. Kim, Intuitionistic (T; S)-normed fuzzy subalgebras of BCK-algebras, J. Chungcheong Math. Soc. 20 (3) (2007), 279-286.
- Y. H. Kim and T. E. Jeong, Intuitionistic fuzzy structure of B-algebras, J. Appl. Math. & Computing 2 (1-2) (2006), 491-500.
- M. A. Malik and M. Touqeer, Intuitionistic fuzzy BCI-commutative ideals in BCI-algebras, Pakistan J. Sci. 64 (4) (2012), 353-358.
- S. M. Mostafa, M. A. A. Naby, and O. R. Elgendy, Intuitionistic fuzzy KU-ideals in KU-algebras, Int. J. Math. Sci. Appl. 1 (3) (2011), 1379-1384.
- N. Palaniappan, R. Devi, and P. S. Veerappan, Intuitionistic fuzzy n-fold BCI-positive implicative ideals in BCI-algebras, Int. J. Fuzzy Math. Syst. 3 (1) (2013), 1-11.
- C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5 (1) (2009), 54-57.
- P. Rangsuk, P. Huana, and A. Iampan, Neutrosophic N-structures over UP-algebras, Neutrosophic Sets Syst. 28 (2019), 87-127.
- A. Satirad and A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math. 12 (2) (2019), 294-331. https://doi.org/10.29020/nybg.ejpam.v12i2.3412
- A. Satirad, P. Mosrijai, and A. Iampan, Formulas for nding UP-algebras, Int. J. Math. Comput. Sci. 14 (2) (2019), 403-409.
- A. Satirad, P. Mosrijai, and A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci. 14 (1) (2019), 17-25.
- B. Satyanarayana and R. D. Prasad, Some results on intuitionistic fuzzy ideals in BCK-algebras, Gen. Math. Notes 4 (1) (2011), 1-15.
- T. Senapati, M. Bhowmik, M. Pal, and B. Davvaz, Atanassov's intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras and ideals in BCK/BCI-algebras, Eurasian Math. J. 6 (1) (2015), 96-114.
- T. Senapati and K. P. Shum, Atanassov's interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras, Discrete Math. Algorithms Appl. 11 (2) (2019), 1950023. https://doi.org/10.1142/s179383091950023x
- J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12 (6) (2016), 739-756.
- M. Songsaeng and A. Iampan, N-fuzzy UP-algebras and its level subsets, J. Algebra Relat. Top. 6 (1) (2018), 1-24.
-
S. Sun and Q. Li, Intuitionistic fuzzy subalgebras (ideals) with thresholds (
${\lambda},{\mu}$ ) of BCI-algebras, Int. J. Math., Comput., Phys. Quantum Eng. 8 (2) (2014), 436-440. - N. Udten, N. Songseang, and A. Iampan, Translation and density of a bipolar- valued fuzzy set in UP-algebras, Ital. J. Pure Appl. Math. 41 (2019), 469-496.
- L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
-
J. Zhan and Z. Tan, Intuitionistic fuzzy
${\alpha}$ -ideals in BCI-algebras, Soochow J. Math. 30 (2) (2004), 207-216.