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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 27Issue 2PP: 303-319 • 2026

Interval-Valued Picture Fuzzy Almost Ideals in Semigroups

Winita Yonthanthum 1* ,
Anusorn Simuen 1 ,
Ronnason Chinram 1
1Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110, Thailand
* Corresponding Author.
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Open Access & Copyright

© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: April 15, 2025 Revised: June 19, 2025 Accepted: August 20, 2025

Abstract

An interval-valued neutrosophic set is a type of neutrosophic sets where the membership, indeterminacy, and non-membership degrees are represented by closed intervals within the unit interval [0, 1]. An interval-valued picture fuzzy set is one of special cases of interval-valued neutrosophic sets. In this paper, we apply interval- valued picture fuzzy sets on almost ideals of semigroups. Moreover, we study a relationship between each almost ideal in a semigroup and their interval-valued picture fuzzifications.

Keywords

Ideals Almost ideals Interval-valued fuzzy sets Interval-valued picture fuzzy sets Interval-valued picture fuzzy almost ideals

References

[1] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353. https://doi.org/10. 1016/S0019-9958(65)90241-X

 

[2] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications 35 (1971), no. 3, 512517.

 

[3] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), no. 2, 133–139. https://doi.org/10.1016/0165-0114(82)90003-3

 

[4] N. Kuroki, On fuzzy semigroups, Information Sciences 53 (1991), no. 3, 203–236. https://doi.org/10.1016/0020-0255(91)90037-U

 

[5] A. L. Narayanan, T. Manikantan, Interval-valued fuzzy ideals generated by an interval-valued fuzzy subset in semigroups, Journal of Applied Mathematics and Computing 20 (2006), 455–464. https: //doi.org/10.1007/BF02831952

 

[6] K. T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia 1 (1983).

 

[7] K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4

 

[8] F. Smarandache. A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, (1999).

 

 [9] B. C. Cuong, V. Kreinovich, Picture fuzzy sets–a new concept for computational intelligence problems, Proceedings of the 2013 Third World Congress on Information and Communication Technologies (WICT),(2013).2013

 

 [10] Y. Yang, C. Liang, S. Ji, T. Liu, Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making, Journal of Intelligent and Fuzzy Systems 29 (2015), no. 4, 17111722. https://doi.org/10.3233/IFS-151648

 

[11] P. Yiarayong, Semigroup characterized by picture fuzzy sets, International Journal of Innovative Computing, Information and Control 16 (2020), no. 6, 2121–2130.

 

[12] O. Grosek, L. Satko, A new notion in the theory of semigroups, Semigroup Forum 20 (1980), no. 3, 233–240. https://doi.org/10.1007/BF02572683

 

[13] J. Ye, Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, Journal of Intelligent and Fuzzy Systems 26 (2014), 165–172. https://doi.org/10.3233/IFS-120724

 

[14] L. Yang, J. Niu, J. Li, Interval-valued neutrosophic sets-based IVNS-RAM method for enhanced security evaluation in computer networks, Neutrosophic Sets and Systems 77 (2025). 479–491.

 

[15] A. Mukherjee, R.Das, Generalized Interval-Valued Neutrosophic Set and Its Application, Transactions on Fuzzy Sets and Systems 4 (2025), no. 2, 1–13. https://doi.org/10.71602/tfss.2025. 1130042

 

[16] P. Liu, M. Munir, T. Mahmood, K. Ullah, Some similarity measures for interval-valued picture fuzzy sets and their applications in decision making, Information, 10 (2019), no. 12, Article number369. https: //doi.org/10.3390/info10120369

 

[17] A. M. Khalil, S. G. Li, H. Garg, H. Li, S. Ma, New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications, IEEE Access 7 (2019),, 51236–51253. https://doi.org/10.1109/ACCESS.2019.2910844

 

[18] S. Zhu, Z. Liu, Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications, Aims Mathematics 8 (2023), no. 12, 29817–29848. https://doi.org/10.3934/ math.20231525

 

[19] Q. Ma, Z. Chen, Y. Tan, J. Wei, An integrated design concept evaluation model based on interval valued picture fuzzy set and improved GRP method, Scientific Reports 14 (2023), no. 1, Article number 8433. https://doi.org/10.1038/s41598-024-57960-9

Cite This Article

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Yonthanthum, Winita, Simuen, Anusorn, Chinram, Ronnason. "Interval-Valued Picture Fuzzy Almost Ideals in Semigroups." International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 2, 2026, pp. 303-319. DOI: https://doi.org/10.54216/IJNS.270226
Yonthanthum, W., Simuen, A., Chinram, R. (2026). Interval-Valued Picture Fuzzy Almost Ideals in Semigroups. International Journal of Neutrosophic Science, Volume 27(Issue 2), 303-319. DOI: https://doi.org/10.54216/IJNS.270226
Yonthanthum, Winita, Simuen, Anusorn, Chinram, Ronnason. "Interval-Valued Picture Fuzzy Almost Ideals in Semigroups." International Journal of Neutrosophic Science Volume 27, no. Issue 2 (2026): 303-319. DOI: https://doi.org/10.54216/IJNS.270226
Yonthanthum, W., Simuen, A., Chinram, R. (2026) 'Interval-Valued Picture Fuzzy Almost Ideals in Semigroups', International Journal of Neutrosophic Science, Volume 27(Issue 2), pp. 303-319. DOI: https://doi.org/10.54216/IJNS.270226
Yonthanthum W, Simuen A, Chinram R. Interval-Valued Picture Fuzzy Almost Ideals in Semigroups. International Journal of Neutrosophic Science. 2026;Volume 27(Issue 2):303-319. DOI: https://doi.org/10.54216/IJNS.270226
W. Yonthanthum, A. Simuen, R. Chinram, "Interval-Valued Picture Fuzzy Almost Ideals in Semigroups," International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 2, pp. 303-319, 2026. DOI: https://doi.org/10.54216/IJNS.270226
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