Fuzzy set theory applied to IUP-algebras
Authors
K. Kuntama
- Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.
P. Krongchai
- Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.
P. Prasertpong
- Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand.
P. Julatha
- Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.
A. Iampan
- Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.
Abstract
In this article, we apply fuzzy set theory to IUP-algebras, introducing four new concepts: fuzzy IUP-subalgebras, fuzzy IUP-filters, fuzzy IUP-ideals, and fuzzy strong IUP-ideals, and examining their properties and relationships.
We also found a relationship between characteristic functions and the four concepts of fuzzy sets.
In addition, the concepts of prime subsets and prime fuzzy sets were also applied.
The notions of upper \(t\)-(strong) level subsets and lower \(t\)-(strong) level subsets of a fuzzy set are introduced in IUP-algebras.
Share and Cite
ISRP Style
K. Kuntama, P. Krongchai, P. Prasertpong, P. Julatha, A. Iampan, Fuzzy set theory applied to IUP-algebras, Journal of Mathematics and Computer Science, 34 (2024), no. 2, 128--143
AMA Style
Kuntama K., Krongchai P., Prasertpong P., Julatha P., Iampan A., Fuzzy set theory applied to IUP-algebras. J Math Comput SCI-JM. (2024); 34(2):128--143
Chicago/Turabian Style
Kuntama, K., Krongchai, P., Prasertpong, P., Julatha, P., Iampan, A.. "Fuzzy set theory applied to IUP-algebras." Journal of Mathematics and Computer Science, 34, no. 2 (2024): 128--143
Keywords
- IUP-algebra
- fuzzy IUP-subalgebra
- fuzzy IUP-filter
- fuzzy IUP-ideal
- fuzzy strong IUP-ideal
- upper \(t\)-(strong) level subsets
- lower \(t\)-(strong) level subsets
MSC
References
-
[1]
S. S. Ahna, H. S. Kim, S.-Z. Song, Y. B. Jun, The (2, 3)-fuzzy set and its application in BCK-algebras and BCI-algebras, J. Math. Comput. Sci., 27 (2022), 118–130
-
[2]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87–96
-
[3]
S. I. Baik, H. S. Kim, On fuzzy k-ideals in semirings, Kangweon-Kyungki Math. J., 8 (2000), 147–154
-
[4]
Y. Bhargavi, T. Eswarlal, Fuzzy -semirings, Int. J. Pure Appl. Math., 98 (2015), 339–349
-
[5]
C. Chanmanee, R. Prasertpong, P. Julatha, N. Lekkoksung, A. Iampan, On external direct products of IUP-algebras, Int. J. Innov. Comput. Inf. Control, 19 (2023), 775–787
-
[6]
M. R. V. Dicen, K. E. Belleza-Fuentes, Fuzzification of the dual B-algebra, Eur. J. Pure Appl. Math., 15 (2022), 1957– 1965
-
[7]
G. Dymek, A. Walendziak, Fuzzy filters of BE-algebras, Math. Slovaca, 63 (2013), 935–946
-
[8]
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
-
[9]
A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Topics, 5 (2017), 35–54
-
[10]
A. Iampan, P. Julatha, P. Khamrot, D. A. Romano, Independent UP-algebras, J. Math. Comput. Sci., 27 (2022), 65–76
-
[11]
K. Is´eki, On BCI-algebras, Math. Semin. Notes, 8 (1980), 125–130
-
[12]
K. Is´eki, S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon., 23 (1978), 1–26
-
[13]
Y. B. Jun, S. Z. Song, Fuzzy set theory applied to implicative ideals in BCK-algebras, Bull. Korean Math. Soc., 43 (2006), 461–470
-
[14]
K. Kalaiarasi, V. Manimozhi, Fuzzy sets in KM-algebras, Gedrag Organ., 33 (2020), 2034–2046
-
[15]
J. Kavikumar, A. B. Khamis, Fuzzy ideals and fuzzy quasi-ideals in ternary semirings, IAENG, Int. J. Appl. Math., 37 (2007), 5 pages
-
[16]
B. Kesorn, K. Maimun, W. Ratbandan, A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math., 34 (2015), 339–364
-
[17]
D. Krishnaswamy, T. Anitha, Fuzzy prime ideals in ternary semirings, Ann. Fuzzy Math. Inform., 7 (2014), 755–763
-
[18]
M. M. K. Rao, Fuzzy left and right bi-quasi ideals of semirings, Bull. Int. Math. Virtual Inst., 8 (2018), 449–460
-
[19]
M. M. K. Rao, Fuzzy filters in ordered -semirings, Casp. J. Math. Sci., 8 (2019), 18–34
-
[20]
M. M. K. Rao, B. Venkateswarlu, Anti fuzzy ideal extension of -semiring, Bull. Int. Math. Virtual Inst., 4 (2014), 135–144
-
[21]
R. Rittichuai, A. Iampan, R. Chinram, P. Singavananda, Almost subsemirings and fuzzifications, Int. J. Math. Comput. Sci., 17 (2022), 1491–1497
-
[22]
A. B. Saeid, M. M. K. Rao, R. K. Kona, N. Rafi, Fuzzy (soft) quasi-interior ideals of semirings, Trans. Fuzzy Sets Syst., 1 (2022), 129–141
-
[23]
J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12 (2016), 739–756
-
[24]
S. Sowmiya, P. Jeyalakshmi, On fuzzy Z-ideals in Z-algebras, Glob. J. Pure Appl. Math., 15 (2019), 505–516
-
[25]
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353
-
[26]
J. Zhan, On properties of fuzzy left h-ideals in hemirings with t-norms, Int. J. Math. Math. Sci., 2005 (2005), 18 pages