Intuitionistic Fuzzy Ideals in $(m‎,n)$-Near Rings

Document Type : Original Scientific Paper

Authors

‎Department of Mathematical Sciences, ‎Yazd University, ‎Yazd‎, ‎Iran

10.22052/mir.2025.255768.1485

Abstract

‎In this article‎, ‎first we review some basic definitions and‎ results about fuzzy sets and intuitionistic fuzzy sets; then we‎ state the definitions of intuitionistic fuzzy (m‎, ‎n)-sub near‎ ‎rings and intuitionistic fuzzy ideals of (m‎, ‎n)-near rings‎, ‎which are generalizations of intuitionistics subrings and‎ ‎intuitionistic fuzzy ideals of rings and near-rings‎, ‎respectively‎. ‎We provide several examples for the definitions and discuss and‎ investigate some results in this respect‎. ‎Finally‎, ‎we investigate‎ the direct product of intuitionistic fuzzy  (m‎, ‎n)-sub near‎ rings of two (m‎, ‎n)-near rings and state and prove some results‎ on these topics‎.

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References

[1] L. A. Zadeh, Fuzzy sets, Inf. Control 8 (1965) 338 - 353, https://doi.org/10.1016/S0019-9958(65)90241-X.
[2] K. T. Atanassov, Intuitionistic Fuzzy sets. In: Theory and Applications, Physica-Verlag, Heidelberg, 1999.
[3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986) 87-96, https://doi.org/10.1016/S01650114(86)800343.
[4] K.T. Atanassov, New operations defined over the intuitionstic fuzzy sets, Fuzzy Sets Syst. 61 (1994) 137 - 142, https://doi.org/10.1016/0165-0114(94)90229-1.
[5] T. Shah, N. Kausar and I. Rehman, Intuitionistic fuzzy normal subrings over a non-associative ring, An. Stiinµ. Univ. "Ovidius” Constanµa Ser. Mat. 20 (2012) 369 - 386, https://doi.org/10.2478/v10309-012-0025-4.
[6] R. Biswas, Intuitionistic fuzzy subgroups, Notes on Intuitionistic Fuzzy Sets 3 (1997) 53 - 60.
[7] E. Szmidt, Distances and Similarities in Intuitionistic Fuzzy Sets, New York: Springer International Publishing, 2014, https://doi.org/10.1007/978-3-319-01640-5.
[8] S. Yilmaz and G. Cuvalcioglu, On study of some intuitionistic fuzzy operators for intuitionistic fuzzy algebraic structures, J. Fuzzy Set. Valued Anal. 2016 (2016) 317 - 325, https://doi.org/10.5899/2016/jfsva-00349.
[9] S. Uma, R. Balakrishnan and T. Tamizh Chelvam,  1,  2-near-rings, Int. J. Algebra 4 (2010) 71 - 79.
[10] J. R. Clay, Nearrings: Geneses and Applications, Oxford, New York, 1992.
[11] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981) 264 - 269, https://doi.org/10.1016/0022247X(81)90164-5.
[12] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512 - 517, https://doi.org/10.1016/0022-247X(71)90199-5.
[13] S. Abou-Zaid, On fuzzy subnear-rings and ideals, Fuzzy Sets and Systems 44 (1991) 139 - 146, https://doi.org/10.1016/0165-0114(91)90039-S.
[14] S. M. Hong, Y. B. Jun and H. S. Kim, Fuzzy ideals in near rings, Bull. Korean Math. Soc. 35 (1998) 455 - 464.
[15] K. H. Kim and Y. B. Jun, Normal fuzzy R-subgroups in near-rings, Fuzzy Sets and Systems 121 (2001) 341 - 345, https://doi.org/10.1016/S0165-0114(00)00022-1.
[16] S. D. Kim and H. S. Kim, On fuzzy ideals of near-rings, Bull. Korean Math. Soc. 33 (1996) 593 - 601.
[17] B. Satyanarayana and K. S. Prasad, Near-Rings, fuzzy ideals and graph theory, CRC Press, New York, 2013.
[18] F. Mohammadi and B. Davvaz, Ideal theory of (m; n)-near rings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73 (2024) 1098 - 1113, https://doi.org/10.31801/cfsuasmas.1494749.
[19] F. Mohammadi and B. Davvaz, An approach to normal fuzzy (m; n)-subnear rings, New Mathematics and Natural Computation, Accepted, https://doi.org/10.1142/S1793005726500018.
[20] Z. Jianming and M. Xueling, Intuitionistic fuzzy ideals of near-rings, Scientiae Mathematicae Japonicae Online (2004) 289 - 293.
[21] Y. B. Jun and S. Z. Song, Intuitionistic fuzzy semi preopen sets and Intuitionistic fuzzy semi precontinuous mappings, J. Appl. Math. Comput. 19 (2005) #467.
Mathematics Interdisciplinary Research
Volume 10, Issue 2
In Progress
June 2025
Pages 199-230

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