Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

Gökhan Çuvalcıoğlu, Sinem Tarsuslu (Yılmaz)


The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.


Intuitionistic fuzzy sets; Intuitionistic fuzzy abstract algebra; Intuitionistic fuzzy function; Intuitionistic fuzzy isomorphism theorems

Full Text:



K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20-23 June, 1983, (Deposed in Central Science & Technology Library of the Bulgarian Academy of Sciences, 1697/84) (in Bulgarian), reprinted in International Journal of Bioautomation 20(S1) (2016), S1 – S6, URL:

G. Birkhoff, Lattice Theory, Colloquium Publications 25, American Mathematical Society, USA (1940), 418 p..

R. Biswas, Intuitionistic fuzzy subgroups, NIFS 3 (1997), 53 – 60,

P. Burillo and H. Bustince, Intuitionistic fuzzy relations (part I), Mathware Soft Computing 2 (1995), 5 – 38,

H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems 78 (1996), 293 – 303, DOI: 10.1016/0165-0114(96)84610-0.

P. M. Cohn, Universal Algebra, D. Reidel Publishing Company, Dordrecht — Holland — Boston — London (1981), 412 p.

G. Deschrijver and E. E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems 136 (2003), 333 – 361, DOI: 10.1016/S0165-0114(02)00269-5.

G. Çuvalcıoglu and S. Yılmaz, Some properties of intuitionistic fuzzy equivalence relations and class trees w.r.t. intuitionistic fuzzy equivalence relations, Advanced Studies in Contemporary Mathematics (Kyungshang) 24(1) (2014), 77 – 86, https: //

G. Çuvalcıoglu and S. Tarsuslu(Yılmaz), Universal algebra in intuitionistic fuzzy set theory, Notes on Intuitionistic Fuzzy Sets 23(1) (2017), 1 – 5,

G. Çuvalcoglu, S. Tarsuslu(Yılmaz), A. Bal and G. Artun, Intuitionistic fuzzy modal operators in intelligent system for pesticide and fertilization, Annals of Fuzzy Mathematics and Informatics 16(1), (2018), 117 – 132, DOI: 10.30948/afmi.2018.16.1.117.

K. Hur, Y. J. Su and W. K. Hee, The lattice of intuitionistic fuzzy congruences, International Mathematical Forum 5(1) (2006), 211 – 236, DOI: 10.12988/imf.2006.06022.

K. Hur, S. Y. Jang and Y. S. Ahn, Intuitionistic fuzzy equivalence relations, Honam Mathematical Journal 27(2) (2005), 163 – 181,

S. Melliani, M. Elomari, R. Ettoussi and L. S Chadli, Intuitionistic fuzzy semigroup, Notes on IFSs 21(2) (2015), 43 – 50,

V. Murali, A Study of Universal Algebra in Fuzzy Set Theory, PhD. Thesis, Department of Mathematics, Rhodes University (1987).

V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems 41(3) (1991), 359 – 369, DOI: 10.1016/0165-0114(91)90138-G.

N. Palaniappan, S. Naganathan and K. Arjunan, A study on intuitionistic L-fuzzy subgroups, Applied Mathematical Sciences 3(53) (2009), 2619 – 2624,

D. Sánchez, P. Melin and O. Castillo, Optimization of modular granular neural networks using a firefly algorithm for human recognition, Engineering Applications of Artificial Intelligence 64 (2017), 172 – 186, DOI: 10.1016/j.engappai.2017.06.007.

P. K. Sharma, (alpha,beta)-cut of intuitionistic fuzzy groups, International Mathematical Forum 53(6) (2011) , 2605 – 2614,

S. Sotirov, E. Sotirova, P. Melin, O. Castilo and K. Atanassov, Modular neural network preprocessing procedure with intuitionistic fuzzy intercriteria analysis method, in: T. Andreasen et al. (editor), Flexible Query Answering Systems 2015, Advances in Intelligent Systems and Computing 400, Springer, Cham, DOI: 10.1007/978-3-319-26154-6_14.

L. Yan, Intuitionistic fuzzy ring and its homomorphism image, 2008 International Seminar on Future BioMedical Information Engineering (2008), 75 – 77, DOI: 10.1109/FBIE.2008.109.

L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338 – 353, DOI: 10.1142/9789814261302_0021.

L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975), 133 – 139, DOI: 10.1016/0020-0255(75)90036-5.

J. Zhan and Z. Tan, Intuitionistic M-fuzzy groups, Soochow Journal of Mathematics 30 (2004), 85 – 90,



  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905