DOI: https://doi.org/10.11568/kjm.2019.27.4.1077

### A novel approach to intuitionistic fuzzy sets in UP-algebras

#### Abstract

The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper $t$-(strong) level subsets and lower $t$-(strong) level subsets in UP-algebras.

#### Keywords

#### Subject classification

03G25; 03E72#### Sponsor(s)

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M. A. Ansari, A. Haidar, and A. N. A. Koam, On a graph associated to UP- algebras, Math. Comput. Appl. 23 (4) (2018), 61. (Google Scholar)

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. (Google Scholar)

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87–96. (Google Scholar)

K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst. 61 (1994), 137–142. (Google Scholar)

M. Bhowmik, T. Senapati, and M. Pal, Intuitionistic L-fuzzy ideals of BG-algebras, Afr. Mat. 25 (2014), 577–590. (Google Scholar)

N. Dokkhamdang, A. Kesorn, and A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 16 (2) (2018), 171–190. (Google Scholar)

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. (Google Scholar)

A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5 (1) (2017), 35–54. (Google Scholar)

A. Iampan, Introducing fully UP-semigroups, Discuss. Math., Gen. Algebra Appl. 38 (2) (2018), 297–306. (Google Scholar)

A. Iampan, Multipliers and near UP-filters of UP-algebras, Manuscript accepted for publication in J. Discrete Math. Sci. Cryptography, July 2019. (Google Scholar)

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. (Google Scholar)

Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideal of BCK-algebras, Internat. J. Math. & Math. Sci. 24 (12) (2000), 839–849. (Google Scholar)

B. Kesorn, K. Maimun, W. Ratbandan, and A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math. 34 (2015), 339–364. (Google Scholar)

K. H. Kim, Intuitionistic (T,S)-normed fuzzy subalgebras of BCK-algebras, J. Chungcheong Math. Soc. 20 (3) (2007), 279–286. (Google Scholar)

Y. H. Kim and T. E. Jeong, Intuitionistic fuzzy structure of B-algebras, J. Appl. Math. & Computing 2 (1-2) (2006), 491–500. (Google Scholar)

M. A. Malik and M. Touqeer, Intuitionistic fuzzy BCI-commutative ideals in BCI-algebras, Pakistan J. Sci. 64 (4) (2012), 353–358. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5 (1) (2009), 54–57. (Google Scholar)

P. Rangsuk, P. Huana, and A. Iampan, Neutrosophic N-structures over UP- algebras, Neutrosophic Sets Syst. 28 (2019), 87–127. (Google Scholar)

A. Satirad and A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math. 12 (2) (2019), 294–331. (Google Scholar)

A. Satirad, P. Mosrijai, and A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci. 14 (2) (2019), 403–409. (Google Scholar)

A. Satirad, P. Mosrijai, and A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci. 14 (1) (2019), 17–25. (Google Scholar)

B. Satyanarayana and R. D. Prasad, Some results on intuitionistic fuzzy ideals in BCK-algebras, Gen. Math. Notes 4 (1) (2011), 1–15. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12 (6) (2016), 739–756. (Google Scholar)

M. Songsaeng and A. Iampan, N-fuzzy UP-algebras and its level subsets, J. Algebra Relat. Top. 6 (1) (2018), 1–24. (Google Scholar)

S. Sun and Q. Li, Intuitionistic fuzzy subalgebras (ideals) with thresholds (λ, μ) of BCI-algebras, Int. J. Math., Comput., Phys. Quantum Eng. 8 (2) (2014), 436–440. [30] 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. (Google Scholar)

L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338–353. (Google Scholar)

J. Zhan and Z. Tan, Intuitionistic fuzzy α-ideals in BCI-algebras, Soochow J. Math. 30 (2) (2004), 207–216. (Google Scholar)

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