Independent UP-algebras
Volume 27, Issue 1, pp 65--76
http://dx.doi.org/10.22436/jmcs.027.01.06
Publication Date: February 12, 2022
Submission Date: November 03, 2021
Revision Date: November 16, 2021
Accteptance Date: January 19, 2022
-
1325
Downloads
-
2859
Views
Authors
A. Iampan
- Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.
P. Julatha
- Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.
P. Khamrot
- Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Phitsanulok, Phitsanulok 65000, Thailand.
D. A. Romano
- International Mathematical Virtual Institute, Kordunaska Street, 78000 Banja Luka, Bosnia and Herzegovina.
Abstract
In this paper, we introduce the concept of a new algebraic structure: independent UP-algebras (in short, IUP-algebras), which is independent of UP-algebras.
We also introduce the concepts of IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals of IUP-algebras and investigate their properties and relationships.
Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.
Share and Cite
ISRP Style
A. Iampan, P. Julatha, P. Khamrot, D. A. Romano, Independent UP-algebras, Journal of Mathematics and Computer Science, 27 (2022), no. 1, 65--76
AMA Style
Iampan A., Julatha P., Khamrot P., Romano D. A., Independent UP-algebras. J Math Comput SCI-JM. (2022); 27(1):65--76
Chicago/Turabian Style
Iampan, A., Julatha, P., Khamrot, P., Romano, D. A.. "Independent UP-algebras." Journal of Mathematics and Computer Science, 27, no. 1 (2022): 65--76
Keywords
- UP-algebra
- IUP-algebra
- IUP-subalgebra
- IUP-filter
- IUP-ideal
- strong IUP-ideal
MSC
References
-
[1]
M. A. Ansari, A. Haidar, A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl., 23 (2018), 12 pages
-
[2]
M. A. Ansari, A. N. A. Koam, A. Haider, Rough set theory applied to UP-algebras, Ital. J. Pure Appl. Math., 42 (2019), 388--402
-
[3]
R. K. Bandaru, N. Rafi, A. Rezaei, On $e${GE}-algebras, Discuss. Math. Gen. Algebra Appl., 41 (2021), 395--409
-
[4]
R. A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar, R. Ameri, On pseudo-BE-algebras, Discuss. Math., Gen. Algebra Appl., 33 (2013), 95--108
-
[5]
R. A. Borzooei, O. Zahiri, Prime ideals in BCI and BCK-algebras, Ann. Univ. Craiova Math. Comput. Sci. Ser., 39 (2012), 266--276
-
[6]
P. Burandate, S. Thongarsa, A. Iampan, Fuzzy sets in UP-algebras with respect to a triangular norm, Konuralp J. Math., 7 (2019), 410--432
-
[7]
N. Dokkhamdang, A. Kesorn, A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 16 (2018), 171--190
-
[8]
A. E. I. Elkabany, M. A. Abdel Naby, S. M. Mostafa, New view of ideals on PU-algebra, Int. J. Comput. Appl., 111 (2015), 9--15
-
[9]
A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Topics, 5 (2017), 35--54
-
[10]
A. Iampan, Introducing fully UP-semigroups, Discuss. Math. Gen. Algebra Appl., 38 (2018), 297--306
-
[11]
A. Iampan, Multipliers and near UP-filters of UP-algebras, J. Discrete Math. Sci. Cryptogr., 24 (2021), 667--680
-
[12]
A. Iampan, M. Songsaeng, G. Muhiuddin, Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math., 13 (2020), 459--471
-
[13]
Y. Imai, K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42 (1966), 19--22
-
[14]
K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26--29
-
[15]
Y. B. Jun, G. Muhiuddin, D. A. Romano, On filters in UP-algebras, a review and some new reflections, J. Int. Math. Virtual Inst., 11 (2021), 35--52
-
[16]
H. S. Kim, Y. H. Kim, On BE-algebras, Sci. Math. Japon., 66 (2007), 113--116
-
[17]
T. Klinseesook, S. Bukok, A. Iampan, Rough set theory applied to UP-algebras, J. Inform. Optim. Sci., 41 (2020), 705--722
-
[18]
P. Mosrijai, A. Iampan, A new branch of bialgebraic structures: UP-bialgebras, J. Taibah Univ. Sci., 13 (2019), 450--459
-
[19]
G. Muhiuddin, Bipolar fuzzy $KU$-subalgebras/ideals of $KU$-algebras, Ann. Fuzzy Math. Inform., 8 (2014), 409--418
-
[20]
G. Muhiuddin, D. Al-Kadi, A. Mahboob, More general form of interval-valued fuzzy ideals of BCK/BCI-algebras, Secur. Commun. Netw., 2021 (2021), 10 pages
-
[21]
C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna, 5 (2009), 54--57
-
[22]
A. Rezaei, A. B. Saeid, A. Radfar, On eBE-algebras, TWMS J. Pure Appl. Math., 7 (2016), 200--210
-
[23]
A. Rezaei, A. B. Saeid, K. Y. S. Saber, On pseudo-CI-algebras, Soft Comput., 23 (2019), 4643--4654
-
[24]
A. Satirad, R. Chinram, A. Iampan, Four new concepts of extensions of KU/UP-algebras, Missouri J. Math. Sci., 32 (2020), 138--157
-
[25]
A. Satirad, R. Chinram, A. Iampan, Pythagorean fuzzy sets in UP-algebras and approximations, AIMS Math., 6 (2021), 6002--6032
-
[26]
A. Satirad, A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math., 12 (2019), 294--331
-
[27]
A. Satirad, P. Mosrijai, A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 403--409
-
[28]
A. Satirad, P. Mosrijai, A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 17--25
-
[29]
S. Sayyad, H. Babaei, A. Rezaei, On pseudo-$e$BE-algebras, Soft Comput., 24 (2020), 7005--7020
-
[30]
T. Senapati, Y. B. Jun, K. P. Shum, Cubic set structure applied in UP-algebras, Discrete Math. Algorithms Appl., 10 (2018), 23 pages
-
[31]
T. Senapati, G. Muhiuddin, K. P. Shum, Representation of UP-algebras in interval-valued intuitionistic fuzzy environment, Ital. J. Pure Appl. Math., 38 (2017), 497--517
-
[32]
J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12 (2016), 739--756
-
[33]
S. Thongarsa, P. Burandate, A. Iampan, Some operations of fuzzy sets in UP-algebras with respect to a triangular norm, Ann. Commun. Math., 2 (2019), 1--10
-
[34]
P. Yiarayong, P. Wachirawongsakorn, A new generalization of BE-algebras, Heliyon, 4 (2018), 11 pages
-
[35]
S. Yuphaphin, P. Kankaew, N. Lapo, R. Chinram, A. Iampan, Picture fuzzy sets in UP-algebras by means of a special type, J. Math. Comput. Sci., 25 (2022), 37--72