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http://dx.doi.org/10.5831/HMJ.2019.41.3.515

FUZZY PROPER UP-FILTERS OF UP-ALGEBRAS  

Songsaeng, Metawee (Department of Mathematics, University of Phayao)
Iampan, Aiyared (Department of Mathematics, University of Phayao)
Publication Information
Honam Mathematical Journal / v.41, no.3, 2019 , pp. 515-530 More about this Journal
Abstract
The concept of fuzzy sets in UP-algebras was first introduced by Somjanta et al. [Fuzzy sets in UP-algebras; 2016]. In this paper, we introduce and study fuzzy proper UP-filters of UP-algebras and prove their generalizations and characteristic fuzzy sets of proper UP-filters. Moreover, we discuss the relations between fuzzy proper UP-filters and their level subsets.
Keywords
UP-algebra; proper UP-filter; fuzzy proper UP-filter;
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1 M. A. Ansari, A. Haidar, and A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl. 23(4) (2018), 61.   DOI
2 N. Dokkhamdang, A. Kesorn, and A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 16(2) (2018), 171-190.   DOI
3 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.   DOI
4 A. R. Hadipour, Generalized fuzzy BF-algebras, Sci. Magna 5(2) (2009), 39-53.
5 A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5(1) (2017), 35-54.
6 A. Iampan, Introducing fully UP-semigroups, Discuss. Math., Gen. Algebra Appl. 38(2) (2018), 297-306.   DOI
7 Y. Imai and K. Iseki, On axiom systems of propositional calculi XIV, Proc. Japan Acad. 42 (1966), 19-22.   DOI
8 K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad. 42(1) (1966), 26-29.   DOI
9 Y. B. Jun, On (${\alpha},{\beta}$)-fuzzy ideals of BCK/BCI-algebras, Sci. Math. Jpn. Online 7 (2004), 101-105.
10 Y. B. Jun, S. S. Ahn, and H. S. Kim, Fuzzy I-ideals in IS-algebras, Commun. Korean Math. Soc. 15(3) (2000), 499-509.
11 Y. B. Jun, E. H. Roh, and H. S. Kim, On fuzzy B-algebras, Czechoslovak Math. J. 52(127) (2002), 375-384.   DOI
12 W. Kaijae, P. Poungsumpao, S. Arayarangsi, and A. Iampan, UP-algebras characterized by their anti-fuzzy UP-ideals and anti-fuzzy UP-subalgebras, Ital. J. Pure Appl. Math. 36 (2016), 667-692.
13 B. Kesorn, K. Maimun, W. Ratbandan, and A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math. 34 (2015), 339-364.
14 M. Akram and K. H. Dar, Fuzzy ideals of K-algebras, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 11-20.
15 J. Neggers and H. S. Kim, On B-algebras, Mat. Vesnik 54 (2002), 21-29.
16 T. Klinseesook, S. Bukok, and A. Iampan, Rough set theory applied to UP-algebras, Manuscript accepted for publication in J. Inf. Optim. Sci., November 2018.
17 M. Akram and K. H. Dar, On fuzzy d-algebras, J. Math., Punjab Univ. 37 (2005), 61-76.
18 A. N. A. Koam, A. Haider, and M. A. Ansari, Pseudo-metric on KU-algebras, Korean J. Math. 27(1) (2019), 131-140.   DOI
19 S. M. Mostafa, M. A. Abd-Elnaby, and M. M. M. Yousef, Fuzzy ideal of KU-algebras, Int. Math. Forum 6(63) (2011), 3139-3149.
20 S. M. Mostafa, M. A. Abd Elnaby, and M. M. M. Yousef, Anti-fuzzy KU ideals of KU-algebras, Int. J. Algebra Stat. 1(1) (2012), 92-99.   DOI
21 P. Poungsumpao, W. Kaijae, S. Arayarangsi, and A. Iampan, Fuzzy UP-ideals and fuzzy UP-subalgebras of UP-algebras in term of level subsets, Int. J. Math. Comput. Sci. 14(3) (2019), 647-674.
22 M. S. Rao, Fuzzy filters of BE-algebras, Int. J. Math. Arch. 4(6) (2013), 181-187.
23 D. A. Romano, Proper UP-filters of UP-algebra, Univ. J. Math. Appl. 1(2) (2018), 98-100.
24 D. A. Romano, Some properties of proper UP-filters of UP-algebras, Fundam. J. Math. Appl. 1(2) (2018), 109-111.
25 A. Satirad, P. Mosrijai, and A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci. 14(2) (2019), 403-409.
26 A. Satirad, P. Mosrijai, and A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci. 14(1) (2019), 17-25.
27 T. Senapati, Y. B. Jun, and K. P. Shum, Cubic set structure applied in UP-algebras, Discrete Math. Algorithms Appl. 10(4) (2018), 1850049.   DOI
28 S. Z. Song, Y. B. Jun, and K. J. Lee, Fuzzy ideals in BE-algebras, Bull. Malays. Math. Sci. Soc. (2) 33(1) (2010), 147-153.
29 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.
30 J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12(6) (2016), 739-756.
31 M. Songsaeng and A. Iampan, N-fuzzy UP-algebras and its level subsets, J. Algebra Relat. Top. 6(1) (2018), 1-24.
32 S. Sripaeng, K. Tanamoon, and A. Iampan, On anti Q-fuzzy UP-ideals and anti Q-fuzzy UP-subalgebras of UP-algebras, J. Inf. Optim. Sci. 39(5) (2018), 1095-1127.   DOI
33 K. Tanamoon, S. Sripaeng, and A. Iampan, Q-fuzzy sets in UP-algebras, Songklanakarin J. Sci. Technol. 40(1) (2018), 9-29.
34 C. Yamini and S. Kailasavalli, Fuzzy B-ideals on B-algebras, Int. J. Math. Arch. 5(2) (2014), 227-233.
35 L. Yonglin and Z. Xiaohong, Fuzzy a-ideals of BCI-algebras, Adv. Math. 31(1) (2002), 65-73.   DOI
36 L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338-353.   DOI