Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

PYTHAGOREAN FUZZY Q-SUBALGEBRA And nil Radical

Document Type : Original Article

Authors
Sirous Jahanpanah 1
Roohallah Daneshpayeh 2
1 Payame Noor University, Tehran, Iran
2 Payame Noor Unoversity,, Tehran, Iran
10.22034/jfsa.2025.513330.1267
Abstract
In this paper, considering the concepts of ‎$Q$-algebra and Pythagorean fuzzy subset, the concepts of ‎$Q$-fuzzy (anti)subalgebra, ‎$Q$-fuzzy Pythagorean subalgebra and null radical of ‎$Q$-fuzzy Pythagorean subalgebra are introduced and it is proved under the conditions that the null radical of ‎$Q$-fuzzy Pythagorean subalgebras is a ‎$Q$-fuzzy Pythagorean subalgebra. Next, with the help of the concept of a level set, the two-way relationship between ‎$Q$-fuzzy Pythagorean subalgebras and ‎$Q$-algebras is discussed and it is shown that ‎$Q$-fuzzy Pythagorean subalgebra is a generalization of ‎$Q$-fuzzy subalgebras. By introducing the combination of Pythagorean fuzzy subalgebras, equivalent conditions for ‎$Q$-fuzzy Pythagorean subalgebras dependent on the combination operation are presented.
Finally, the relationship between the isomorphic image of the null radical of the Pythagorean fuzzy subalgebra $Q$ and the null radical of the isomorphic image of the Pythagorean fuzzy subalgebra $Q$ is discussed.
Keywords
Q-fuzzy subalgebra
anti fuzzy Q-subalgebra
Pythagorean fuzzy Q-subalgebra
nil radical Pythagorean Q-subalgebra
Subjects
[1]    H. K. Abdullah, H. K. Jawad, New Types of Ideals in Q-algebra, J. K. U, 16 (3) ( 2018) 9–21.
[2]    K. T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst, 20 (1986) 87–96.
[3]    K. Iséki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 125–130.MR 81k:06018a. Zbl 0434.03049.
[4]    K. Iséki and S. Tanaka, An introduction to the theory of BCK -algebras, Math. Japon. 23 (1978), no. 1, 1–26. MR 80a:03081. Zbl 385.03051.
[5]    M. Kavitha, & R. I. Hepzibah, New operations on Pythagorean Neutrosophic Fuzzy Sets, TWMS Journal of Applied and Engineering Mathematics, 15(3) (2025) 560-576.
 
[6]    J. N. Mordeson, D. S. Malik, Fuzzy Commutative Algebra, World Scientific Publishing Co. Pte. Ltd., 1998.
[7]    S. M. Mostafa , M. A. A. Naby, O. R. Elgendy, Fuzzy Q-ideals in Q-algebras, World Applied Programming 2 (2) (2012) 69–80.
[8]    S. M. Mostafa, M. A. A. Elnaby and O. R. Elgendy, Interval-Valued Fuzzy Q-Ideals in Q-Algebras, International Journal of Algebra, 5 (27) (2011) 1337–134.
[9]    J. Negrees, S. S. Ahn, and H. S. Kim, ON Q-Algebras, IJMMS, 27 (12) (2001) 749–757.
[10]    M.Rahima, F. Amina, K. Shahb, T. Abdeljawadb, S. Ahmadc, Some distance measures for pythagorean cubic fuzzy sets: Application selection in optimal treatment for depression and anxi- ety, MethodsX, 12 (2024) 102678.
[11]    A. B. Saeid, R. Daneshpayeh, S. Jahanpanah, On L-sub Q-algebras. Soft Computing, 28 (2024) 12477-12490.
[12]    R. R. Yager, Pythagorean fuzzy subsets, In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 36286152.
[13]    R. R. Yager, Pythagorean membership grades in multi-criteria decision making. Technical Report MII-3301. New Rochelle, NY: Machine Intelligence Institute, Iona College; 2013.
[14]    L. A. Zadeh, Fuzzy sets, Information Control, 8 (3) (1965) 338–353.
[15]    D. Wang, S. Letchmunan, J. Liao, H. Qiu, Z. Liu, Construction of New Similarity Measures for Complex Pythagorean Fuzzy Sets and Their Applications in Decision-Making Problems, Journal of Intelligent Decision Making and Information Science Volume 2, (2025) 156-176.
Fuzzy Systems and its Applications
Volume 7, Issue 2 - Serial Number 15
Open Access Statement
December 2024
Pages 245-269

  • Receive Date 20 March 2025
  • Revise Date 01 May 2025
  • Accept Date 27 May 2025