Rough Pythagorean fuzzy ideals in ternary semigroups
Volume 20, Issue 4, pp 302--312
http://dx.doi.org/10.22436/jmcs.020.04.04
Publication Date: February 28, 2020
Submission Date: August 20, 2019
Revision Date: February 02, 2020
Accteptance Date: February 04, 2020
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Authors
Ronnason Chinram
- Algebra and Applications Research Unit, Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand.
- Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand.
Thammarat Panityakul
- Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand.
Abstract
A ternary semigroup is a nonempty set equipped with an associative ternary operation. A Pythagorean fuzzy set is one of the generalizations of the fuzzy set. The aim of this paper is to study rough Pythagorean fuzzy ideals in ternary semigroups. This idea is extended to the lower and upper approximations of Pythagorean fuzzy ideals.
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ISRP Style
Ronnason Chinram, Thammarat Panityakul, Rough Pythagorean fuzzy ideals in ternary semigroups, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 302--312
AMA Style
Chinram Ronnason, Panityakul Thammarat, Rough Pythagorean fuzzy ideals in ternary semigroups. J Math Comput SCI-JM. (2020); 20(4):302--312
Chicago/Turabian Style
Chinram, Ronnason, Panityakul, Thammarat. "Rough Pythagorean fuzzy ideals in ternary semigroups." Journal of Mathematics and Computer Science, 20, no. 4 (2020): 302--312
Keywords
- Fuzzy sets
- Pythagorean fuzzy sets
- rough sets
- ternary semigroups
MSC
References
-
[1]
M. A. Ansari, N. Yaqoob, $T$-rough ideals in ternary semigroups, Int. J. Pure Appl. Math., 86 (2013), 411--424
-
[2]
R. Chinram, Rough prime ideals and rough fuzzy prime ideals in gamma-semigroups, Commun. Korean Math. Soc., 24 (2009), 341--351
-
[3]
H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, Int. J. Intell. Syst., 31 (2016), 886--920
-
[4]
H. Garg, Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making, J. Exper. Theor. Artif. Intell., 30 (2018), 763--794
-
[5]
A. Hussain, T. Mahmood, M. I. Ali, Rough Pythagorean fuzzy ideals in semigroups, Comput. Appl. Math., 38 (2019), 15 pages
-
[6]
A. Iampan, Some properties of ideal extensions in ternary semigroups, Iran. J. Math. Sci. Inform., 8 (2013), 67--74
-
[7]
C. Jirojkul, R. Chinram, R. Sripakorn, Roughness of quasi-ideals in $\Gamma$-semigroups, JP J. Algebra Number Theory Appl., 12 (2008), 113--120
-
[8]
Y. B. Jun, Roughness of gamma-subsemigroups/ideals in gamma-semigroups, Bull. Korean Math. Soc., 40 (2003), 531--536
-
[9]
N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Paul., 28 (1980), 17--21
-
[10]
N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5 (1981), 203--215
-
[11]
N. Kuroki, Rough ideals in semigroups, Inform. Sci., 100 (1997), 139--163
-
[12]
D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math., 54 (1932), 329--338
-
[13]
J. Łoś, On the extending of models $(I)^*$, Fund. Math., 42 (1955), 38--54
-
[14]
S. Naz, S. Ashraf, M. Akram, A Novel Approach to Decision-Making with Pythagorean Fuzzy Information, Mathematics, 6 (2018), 28 pages
-
[15]
Z. Pawlak, Rough sets, J. Comput. Inform. Sci., 11 (1982), 341--356
-
[16]
X. D. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Int. J. Intell. Syst., 30 (2015), 1133--1160
-
[17]
R. Prasertpong, M. Siripitukdet, On rough sets induced by fuzzy relations approach in semigroups, Open Math., 16 (2018), 1634--1650
-
[18]
P. Ratanaburee, T. Kaewnoi, R. Chinram, Straddles on ternary semigroups, J. Math. Computer Sci., 19 (2019), 246--250
-
[19]
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512--517
-
[20]
B. Thongkam, T. Changphas, On two-sided bases of ternary semigroups, Quasigroups Related Systems, 23 (2015), 319--324
-
[21]
R. R. Yager, Pythagorean fuzzy subsets, Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (Edmonton, Canada), 2013 (2013), 57--61
-
[22]
R. R. Yager, A. M. Abbasov, Pythagorean member grades, complex numbers, and decision making, Int. J. Intell. Syst., 28 (2013), 436--452
-
[23]
L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338--353