Intuitionistic multi fuzzy ideals of near-rings

  • Nadia Batool Department of Mathematics, University of Baltistan Skardu, Gilgit Baltiistan 16100, Pakistan
  • Sadaqat Hussain Department of Mathematics, University of Baltistan Skardu, Gilgit Baltiistan 16100, Pakistan
  • Nasreen Kausar Department of Mathematics, Faculty of Arts ans Sciences, Yildiz Technical University, Istanbul, Turkey
  • Mohammed Munir Department of Mathematics, Government Postgraduate College 22010, Khyber Pakhtunkhwa, Pakistan
  • Rita Yi Man Li Department of Economics and Finance, Hong Kong Shue Yan University, Hong Kong, China
  • Salma Khan Department of Mathematics and Statistics Hazara University Mansehra, 21120, Khyber Pakhtunkhwa, Pakistan
Keywords: Intuitionistic Fuzzy Set, Near-ring, Fuzzy Multi Near-ring, Intuitionistic multi fuzzy Near-ring, Ideals, fuzzy multi ring


Real-world data is often partial, uncertain, or incomplete. Decision-making based on data as such can be addressed by fuzzy sets and related systems. This article studies the intuitionistic multi-fuzzy sub-near rings and Intuitionistic multi-fuzzy ideals of near rings. It presents some of the elementary operations and relations defined on these structures. The concept of level subsets and support of the Intuitionistic multi-fuzzy sub-near ring is also presented. It looks into and demonstrates a few characteristics of intuitionistic multi-fuzzy near-rings and ideals. This research advances fuzzy set theory, which is often applied to problems involving pattern recognition and multiple criterion decision-making. Thus, the results may be beneficial to artificial intelligence related research. Alternatively, the intuitionistic multi-fuzzy approach may be applied to vector spaces and modules or extended to inter-valued fuzzy systems.


Download data is not yet available.


Abbas, S., Hussain, Z., Hussain, S., Sharif, R., & Hussain, S. (2021). Intuitionistic fuzzy entropy and its applications to multicriteria decision making with IF-TODIM. Journal of mechanics of continua and mathematical sciences, 16(7), 99–119.

Abdullah, L. (2013). Fuzzy multi criteria decision making and its applications: A brief review of category. Procedia-Social and Behavioral Sciences, 97, 131–136. DOI:

Abou-Zaid, S. (1991). On fuzzy subnear-rings and ideals. Fuzzy Sets and Systems, 44(1), 139–146. DOI:

Al Tahan, M., Hoskova-Mayerova, S., & Davvaz, B. (2021). An approach to fuzzy multi-ideals of near rings. Journal of Intelligent & Fuzzy Systems, Preprint, 1–11. 10.3233/JIFS-202914.

Al-Husban, A. (2021). Multi-fuzzy hypergroups. Italian Journal of Pure and Applied Mathematics, 46, 382–390.

Ashraf, A., Ullah, K., Hussain, A., & Bari, M. (2022). Interval-Valued Picture Fuzzy Maclaurin Symmetric Mean Operator with application in Multiple Attribute Decision-Making. Reports in Mechanical Engineering, 3(1), 301–317. DOI:

Asif, A., Aydi, H., Arshad, M., Rehman, A., & Tariq, U. (2020). Picture Fuzzy Ideals of Near-Rings. Journal of Mathematics, 2020.

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems 20 (1), 87-96. DOI:

Broumi, S., Ajay, D., Chellamani, P., Malayalan, L., Talea, M., Bakali, A., Schweizer, P., & Jafari, S. (2022). Interval Valued Pentapartitioned Neutrosophic Graphs with an Application to MCDM. Operational Research in Engineering Sciences: Theory and Applications, 5(3), 68–91. DOI:

Broumi, S., Sundareswaran, R., Shanmugapriya, M., Nordo, G., Talea, M., Bakali, A., & Smarandache, F. (2022). Interval-valued fermatean neutrosophic graphs. Decision Making: Applications in Management and Engineering, 5(2), 176–200. DOI:

Dresher, M., & Ore, O. (1938). Theory of Multigroups. American Journal of Mathematics, 60(3), 705–733. DOI:

Fathi, M., & Salleh, A. R. (2009). Intuitionistic fuzzy groups. Asian Journal of Algebra, 2(1), 1–10. DOI:

Gulzar, M., Alghazzawi, D., Mateen, M. H., & Kausar, N. (2020). A certain class of t-intuitionistic fuzzy subgroups. IEEE Access, 8, 163260–163268.

Gulzar, M., Mateen, M. H., Alghazzawi, D., & Kausar, N. (2020). A novel application of complex intuitionistic fuzzy sets in group theory. IEEE Access, 8, 196075–196085.

Hoskova-Mayerova, S., & Al Tahan, M. (2021). Anti-Fuzzy Multi-Ideals of Near Ring. Mathematics, 9(5), 494.

Hur, K., Jang, S.-Y., & Kang, H.-W. (2005). Intuitionistic fuzzy ideals of a ring. The Pure and Applied Mathematics, 12(3), 193–209.

Hussain, S., Hussain, S., Rahaman, S., & Abbas, S. (2022). Fuzzy Normed Near-rings and its Ideals. Journal of Xi’an Shiyou University, Natural Science Edition, 18(9), 32–36.

Kahraman, C. (2008). Multi-criteria decision-making methods and fuzzy sets. In Fuzzy multi-criteria decision making, 1–18. Springer. DOI:

Kausar, N. (2019). Direct product of finite intuitionistic anti fuzzy normal subrings over non-associative rings. European Journal of Pure and Applied Mathematics, 12(2), 622–648.

Kausar, N., Alesemi, M., & Munir, M. (2020). Characterizations of Non-Associative Ordered Semigroups by Their Intuitionistic Fuzzy Bi-Ideals. Discontinuity, Nonlinearity, and Complexity, 9(2), 257–275.

Kausar, N., & Waqar, M. A. (2019). Characterizations of non-associative rings by their intuitionistic fuzzy bi-ideals. European Journal of Pure and Applied Mathematics, 12(1), 226–250.

Kousar, S., Aslam, F., Kausar, N., & Gaba, Y. U. (2021). Semigroup of finite-state deterministic intuitionistic fuzzy automata with application in fault diagnosis of an aircraft twin-spool turbofan engine. Journal of Function Spaces, 2021, 1–10.

Kousar, S., Saleem, T., Kausar, N., Pamucar, D., & Addis, G. M. (2022). Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3. Computational Intelligence and Neuroscience, 2022, 1–11.

Rahman, S., & Saikia, H. K. (2012). Some aspects of Atanassov’s intuitionistic fuzzy submodules. Int. J. Pure and Appl. Mathematics, 77(3), 369–383.

Riaz, A., Kousar, S., Kausar, N., Pamucar, D., & Addis, G. (2022a). Codes over Lattice-Valued Intuitionistic Fuzzy Set Type-3 with Application to the Complex DNA Analysis. Complexity, 2022, 1–12.

Riaz, A., Kousar, S., Kausar, N., Pamucar, D., & Addis, G. M. (2022b). An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3-Submodules. Computational Intelligence and Neuroscience, 2022, 1–13.

Shah, T., Kausar, N., & Rehman, I. (2012). Intuitionistic fuzzy normal subrings over a non-associative ring. Analele Universitatii "Ovidius" Constanta-Seria Matematica, 20(1), 369–386. DOI:

Shinoj, T. K., Baby, A., & Sunil, J. J. (2015). On some algebraic structures of fuzzy multisets. Annals of Fuzzy Mathematics and Informatics, 9(1), 77–90.

Sujatha, L. (2014). Multi fuzzy subrings and ideals. Annals of Fuzzy Mathematics and Informatics, 8(3), 385–392.

Taghieh, A., Mohammadzadeh, A., Zhang, C., Kausar, N., & Castillo, O. (2022). A type-3 fuzzy control for current sharing and voltage balancing in microgrids. Applied Soft Computing, 129, 1–13.

Yager, R. R. (1986). On the theory of bags. International Journal of General System, 13(1), 23–37. DOI:

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. DOI:

Zhan, J., & Ma, X. (2005). Intuitionistic fuzzy ideals of near-rings. Scientiae Mathematicae Japonicae, 61(2), 219–223.

Zhumadillayeva, A., Orazbayev, B., Santeyeva, S., Dyussekeyev, K., Li, R. Y. M., Crabbe, M. J. C., & Yue, X.-G. (2020). Models for oil refinery waste management using determined and fuzzy conditions. Information, 11(6), 299.

How to Cite
Batool, N., Hussain, S., Kausar, N., Munir, M., Li, R. Y. M., & Khan, S. (2023). Intuitionistic multi fuzzy ideals of near-rings. Decision Making: Applications in Management and Engineering.
Regular articles