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The Journal of Information and Optimization Sciences (JIOS) is a world leading journal publishing high quality, rigorously peer-reviewed original research in all mathematically-oriented theoretical and applied topics in information sciences, optimization sciences and related areas since 1980. Subjects include but are not limited to: • Information Sciences • Optimization Sciences • Control Theory • Operational Research • Decision Sciences • Information Theory • Information Technology • Computer Networks and Communications • Mathematical Programming • Modelling and Simulation • Database Management • Applications to Engineering Sciences • Applications to Technology

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Open Access Research Article

Intuitionistic fuzzy equivalence relations and ideals on rings under norms

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pp. 1301–1312Vol. 47Issue 4April 2026DOI: 10.47974/JIOS-1422XML
Received:
06 Dec 2022
Published Online:
01 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1422
Pages:
1301–1312

Abstract

In this paper, we investigate norms defined on intuitionistic fuzzy equivalence relations, intuitionistic fuzzy congruence relations, and intuitionistic fuzzy ideals of rings. We explore their properties and structural characteristics, as well as their behavior under ring homomorphisms.

Keywords

Subject Classifications

13Axx03E7208A3047A3020K30

References

[1] L. A. Zadeh, “ Fuzzy sets”,  inform. and Control, vol. 8, pp. 338-353 (1965).[2] J. A. Goguen, “L-fuzzy sets”,  J. Math. Anal. Appl., vol. 18, pp. 145-174 (1967).[3] E. Sanchez, “Resolution of composite fuzzy relation equation”,  Inform. and Control , vol. 30, pp. 38-48 (1976).[4] C. Nemitz, “ Fuzzy relations and fuzzy function”,  Fuzzy Sets and Systems, vol. 19, pp. 177-191 (1986).[5] V. Murali, “ Fuzzy equivalence relation”,  Fuzzy Sets and Systems, vol. 30, pp. 155-163 (1989).[6] M. Samhan, “ Fuzzy congruences on semigroups”,  Inform. Sci. , vol. 74, pp. 165-175 (1993).[7] W. Liu, “Fuzzy invariant subgroups and fuzzy ideals”,  Fuzzy Sets and Systems, vol. 8, pp.133-139 (1982).[8] K. T. Atanassov, “Intuitionistic fuzzy sets”,  Fuzzy Sets and Systems, vol. 20, pp. 87-96 (1986).[9] K. T. Atanassov, “New operations defined over the intuitionistic fuzzy sets”,  Fuzzy Sets and Systems, vol. 61, pp. 137-142 (1994).[10] K. T. Atanassov, “Intuitionistic Fuzzy Sets Theory and Applications”, Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg (1999).[11] H. H. Abbass and K. O. Kadem, “On pseudo intuitionistic fuzzy ideal of pseudo BH-algebra”,  Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 6, pp. 1595-1600 (2021).[12] A. T. Hameed, M. S. M. Zabiba and N. H. Malik, “Magnified translation of intuitionistic fuzzy AT-ideals on AT-algebras”,  Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 6, pp. 1645-1650 (2021).[13] T. Senapati, M. Bhowmik, M. Pal and K. P. Shum, “Characterization of intuitionistic fuzzy BG-subalgebras of BG-algebras”,  Journal of Discrete Mathematical Sciences and Cryptography, vol. 21, pp. 1549-1558 (2018).[14] S .K. Bhakat and P. Das, “Fuzzy subrings and ideals redefined”,  Fuzzy Sets and Systems, vol. 81, pp. 383-393 (1996).[15] R. Rasuli, “t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras”,  Mathematical Analysis and its Contemporary Applications, vol 4, no. 2, pp. 17-34 (2022).[16] R. Rasuli, “T-fuzzy subbigroups and normal T-fuzzy subbigroups of bigroups”,  J. of Ramannujan Society of Mathematics and Mathematical Sciences, vol. 9, no. 2, pp. 165-184 (2022).[17] R. Rasuli, M. A. Hashemi and B. Taherkhani, “S-norms and Anti fuzzy ideals of BCI-algebras”, 10th National Mathematics Conference of the Payame Noor University, Shiraz, May (2022).[18] R. Rasuli, B. Taherkhani and H. Naraghi, “T-fuzzy SU-subalgebras”, 10th National Mathematics Conference of the Payame Noor University, Shiraz, May (2022).[19] R. Rasuli, “A study of T-fuzzy multigroups and direct preoduct of them”, 1th National Conference on Applied Reserches in Basic Sciences( Mathematics, Chemistry and Physics) held by University of Ayatolla Boroujerdi, Iran, during May 26-27 (20220.[20] R. Rasuli, “S - (M,N)-fuzzy subgroups”, 1th National Conference on Applied Reserches in Basic Sciences( Mathematics, Chemistry and Physics) held by University of Ayatolla Boroujerdi, Iran, during May 26-27 (2022).[21] R. Rasuli, “Intuitionistic fuzzy BCI-algebras (implicative ideals, closed implicative ideals, commutative ideals) under norms”,   Mathematical Analysis and its Contemporary Applications, vol. 4, no. 3, pp. 17-34 (2022).[22] R. Rasuli, “ Fuzzy d-algebras under t-norms”,  Eng. Appl. Sci. Lett. (EASL), vol. 5, no. 1, pp. 27-36 (2022).[23] R. Rasuli, “ Fuzzy vector spaces under norms”,  Annals of Mathematics and Computer Science, vol. 9, pp. 7-24 (2022).[24] R. Rasuli, “T-fuzzy G-submodules”,   Scientia Magna, vol. 17, no. 1, pp. 107-118 (2022).[25] R. Rasuli, “Anti Fuzzy Congruence on Product Lattices”, 7^th International Congerence on Combinatotcs, Crytography, Computer Science and Computing held by Iran University of Science and Technology, Iran,Tehran, during November 16-17 (2022).[26] M. T. Abu Osman, “On some products of fuzzy subgroups”,  Fuzzy Sets and Systems, vol. 24, pp. 79-86 (1987).
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