Some Characterization of Fermatean Fuzzy L-ring Ideals
DOI:
https://doi.org/10.22105/6tbdq214Keywords:
Intuitionistic fuzzy sets, Pythagorean fuzzy sets, Fermatean fuzzy sets, Fermatean fuzzy lattice, Fermatean fuzzy L-ring idealAbstract
The Fermatean fuzzy set (FFS) represents a robust approach for addressing ambiguity, effectively managing issues that remain unresolved by Intuitionistic fuzzy set and Pythagorean fuzzy set concepts. Due to its practical utility and significant impact on tackling real-world challenges across various domains, FFS has spurred extensive research. This study defines Fermatean fuzzy sublattice and Fermatean fuzzy lattice. Additionally, it introduces Fermatean fuzzy L-ring ideals. The paper explores the concept of homomorphism within Fermatean fuzzy sets. Furthermore, it investigates important findings concerning the image and pre-image of Fermatean fuzzy L-ring ideals, utilizing properties of infimum and supremum. The results are illustrated through pertinent numerical examples.
References
A. K. Adak, Interval-Valued Intuitionistic Fuzzy Subnear Rings, Handbook of Research on Emerging Applications of Fuzzy
Algebraic Structures IGI-Global, (2020) 213-224.
N. Ajmal, and K. V. Thomas, The Lattice of Fuzzy ideals of a ring. Fuzzy sets and Systems, 371-379, (1995).
N. Ajmal, Homomorphism of fuzzy Subgroups, Correspondents theorem, Fuzzy Sets and Systems, 61(1994) 329-339.
K. T. Atanassov, Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1) (1986), 87-96.
K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets. Fuzzy sets and Systems, 61, (1994), 137-142.
G. Brikhoff, Lattice Theory, Published by American Mathematical Theory Providence , Rhode, Island, (1967).
P. Burillo and H. Bustince, Intuitionistic fuzzy relations (Part I), Mathware and computing, 2: 5–38, 1995.
P. Burillo and H. Bustince, Intuitionistic fuzzy relations (Part II), Effect of Atanassov’s operators on the properties of the bi
fuzzy relations, Mathware and computing, 2:117–148, 1995.
K. Chandrasekharan Rao and Swaminathan, Anti-Homomorphism in Near Rings, Jr of Inst. of maths and computer sciences
(Math.Ser), Vol.2 (2006), 83-88.
Fang Jin-Xuan, Fuzzy Homomorphism and Fuzzy isomorphism,Fuzzy Sets and Systems, 63(1994), 237-242.
A. A. M. Hassan, On Fuzzy Rings and Fuzzy Homomorphisms, The Journal of fuzzy Mathematics, Vol.7, No.2, 1999.
K. Hur, Y. S. Ahn and DS. Kim The Lattice of Intuitionistic Fuzzy Ideals of a Ring, Journal of Appl.math and Computing ,
(12), (2005) No, 12pp, 465-486.
K. Hur, S. Y. Jang and H. W. Kang, Intuitionistic Fuzzy Ideals of a Ring, J. Korea Soc Math. Educ Ser. B: Pure Appl. Math.,
(3),(2005), 193-209.
K. Hur, H. W. Kang, and H. K. Song, Intuitionistic Fuzzy Sub- groups and Subrings,Honam Math J. 25 (1), (2003), 19-41.
K. H. Kim and Y. B. Jun, Intuitionistic fuzzy ideals of semigroups, Indian J. Pure Appl. Math. 33(4) (2002) 443-449.
K. H. Kim and Y.B. Jun, Intuitionistic fuzzy interior ideals of semigroups, Int. J. Math. Math. Sci. 27 (5) (2001) 261-267.
K. H. Kim and J. G. Lee, On fuzzy bi-ideals of semigroups, Turk. J. Math. 29 (2005) 201–210.
S. P. Kuncham, S. Bhavanari, Fuzzy prime ideal of a gamma near ring. Soochow Journal of Mathematics 31 (1) (2005) 121-129.
K. Meena, and K. V. Thomas, Intuitionistic L-fuzzy Subrings, International Mathematical Forum, 6(52), (2011), 2561-2572.
R. Natrajan, S. Moganavalli, Fuzzy Sublattice Ordered Rings, International journals of contemporary Mathematical Sciences,
(13), (2012), 625-630.
D. M. Olson, On the Homomorphism for Hemirings, IJMMS, 1(1978), 439-445.
Palaniappan.N and K.Arjunan, The Homomorphism Anti- Homomorphism of a Fuzzy and Anti-Fuzzy ideals, Varahmihir
journal of mathematical sciences, vol.6 no.1(2006), 181-188.
S. K. Sardar, S. K. Majumder and M. Mandal, Atanassov’s intuitionistic fuzzy ideals of Γ-semigroups, Int. J. Algebra 5(7)
(2011) 335-353.
KR. Sasireka, KE. Sathappan and B. Chellapa Intuitionistic Fuzzy l- filters, International Journal of Mathematics and its
applications, 4(2c), (2016), 171-178.
T. Senapati, T. and R. R. Yager, Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy
WPM in multiple criteria decision making, Informatica, 30(2) 391-412, (2019).
A. Sheikabdullah and K. Jeyaraman, Anti-homomorphism in fuzzy ideals of rings, Int. J. Contemp. Math. Sciences, 5(55),
(2010), 2717-2721.
K. V. Thomas and L. S. Nair, Intuitionistic fuzzy sublattices and ideals, Fuzzy Information and Engineering, 3(2011), 321–331.
K. V. Thomas and L. S. Nair, Rough intuitionistic fuzzy sets in a lattice, International Mathematical Forum, 6(2011), 1327–1335.
B. K. Tripathy, M. K. Satapathy and P. K. Choudhury, Intuitionistic fuzzy lattices and intuitionistic fuzzy Boolean algebras,
International Journal of Engineering and Technology, 5(2013), 2352–2361.
R. R. Yager, Abbasov AM. Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst 28 (2013)
-452.
R. R. Yager, Pythagorean fuzzy subsets. In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton,
Canada, (2013) 57-61.
G. J. Wang, Order-Homomorphism on fuzzy sets, Fuzzy sets and Systems , 12 (1984), 281-288.
L. A. Zadeh, Fuzzy Sets, Inform and Control, 8(1965) 338-353.