A new look of interval-valued intuitionistic fuzzy sets in ordered AG-groupoids with applications

Faisal Yousafzai; Muhammad Danish Zia; Mohammed M. Khalaf; Rashad Ismail; Faisal Yousafzai; Muhammad Danish Zia; Mohammed M. Khalaf; Rashad Ismail

doi:10.3934/math.2023308

AIMS Mathematics

2023, Volume 8, Issue 3: 6095-6118. doi: 10.3934/math.2023308

Previous Article Next Article

Research article Special Issues

A new look of interval-valued intuitionistic fuzzy sets in ordered AG-groupoids with applications

1.
Department of Basic Sciences and Humanities, National University of Sciences and Technology, Islamabad, Pakistan
2.
Department of Mathematics, Higher Institute of Engineering and Technology, King Marriott, P.O. Box 3135, Alexandria 23713, Egypt
3.
Department of Mathematics, Faculty of Science and Arts, Muhayl Assir 61913, King Khalid University, Saudi Arabia
4.
Departments of Mathematics and Computer, Faculty of Science, Ibb University, Ibb 70270, Yemen

Received: 19 September 2022 Revised: 05 December 2022 Accepted: 19 December 2022 Published: 29 December 2022
MSC : 03E72, 08A72, 91B06

The main purpose of this article is to utilize mathematical tools to rank alternatives for a decision making problem. In this regard, we developed different types of interval-valued intuitionistic fuzzy (IVIF) score ideals through unit-valued score (accuracy) functions. We used IVIF-score left (right) ideals to characterize an intra-regular class of an ordered Abel-Grassmann's-grououpoid (AG-groupoid) which is a semilattice of left simple AG-groupoids. We also established a connection between IVIF-score (0, 2)-ideals and IVIF-score left (right) ideals. Finally, we demonstrated how to use the interval valued intuitionistic fuzzy score $ (0, 2) $-ideals to identify the most suitable alternative in a decision making problem, and also explain how it can be applied to a problem of selecting a warehouse.
- interval-valued intuitionistic fuzzy set,
- uv-score function,
- left invertive law,
- semilattice,
- intra-regularity
Citation: Faisal Yousafzai, Muhammad Danish Zia, Mohammed M. Khalaf, Rashad Ismail. A new look of interval-valued intuitionistic fuzzy sets in ordered AG-groupoids with applications[J]. AIMS Mathematics, 2023, 8(3): 6095-6118. doi: 10.3934/math.2023308

Related Papers:

Abstract

The main purpose of this article is to utilize mathematical tools to rank alternatives for a decision making problem. In this regard, we developed different types of interval-valued intuitionistic fuzzy (IVIF) score ideals through unit-valued score (accuracy) functions. We used IVIF-score left (right) ideals to characterize an intra-regular class of an ordered Abel-Grassmann's-grououpoid (AG-groupoid) which is a semilattice of left simple AG-groupoids. We also established a connection between IVIF-score (0, 2)-ideals and IVIF-score left (right) ideals. Finally, we demonstrated how to use the interval valued intuitionistic fuzzy score $ (0, 2) $-ideals to identify the most suitable alternative in a decision making problem, and also explain how it can be applied to a problem of selecting a warehouse.

References

[1]	T. Asif, F. Yousafzai, A. Khan, K. Hila, Ideal theory in ordered AG-groupoids based on double framed soft sets, J. Mult.-Valued Log. S., 33 (2019), 27–49.
[2]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1007/978-3-7908-1870-3_1 doi: 10.1007/978-3-7908-1870-3_1
[3]	K. T. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst., 31 (1989), 343– 349.
[4]	X. S. Cai, L. G. Han, Some induced Einstein aggregation operators based on the data mining with interval-valued intuitionistic fuzzy information and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 27 (2014), 331–338. https://doi.org/10.3233/IFS-131000 doi: 10.3233/IFS-131000
[5]	Z. T. Chen, X. D. Yang, Y. Y. Zhu, Approach to multiple attribute decision making with interval-valued intuitionistic fuzzy information and its application, J. Intell. Fuzzy. Syst., 29 (2015), 489–497. https://doi.org/10.3233/IFS-141201 doi: 10.3233/IFS-141201
[6]	D. H. Hong, C. H. Choi, Multicriteria fuzzy decision making problems based on vague set theory, Fuzzy Set. Syst., 114 (2000), 103–113. https://doi.org/10.1016/S0165-0114(98)00271-1 doi: 10.1016/S0165-0114(98)00271-1
[7]	H. Kamacı, S. Petchimuthu, E. Akçetin, Dynamic aggregation operators and Einstein operations based on interval-valued picture hesitant fuzzy information and their applications in multi-period decision making, Comput. Appl. Math., 40 (2021), 1–52.
[8]	H. Kamacı, Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications, Complex Intell. Syst. 8 (2022), 1281–1305.
[9]	H. Kamacı, Linear Diophantine fuzzy algebraic structures, J. Amb. Intel. Hum. Comput., 12 (2021), 10353–10373.
[10]	M. S. Kamran, Structural properties of LA-semigroups, M. Phil Thesis, Quaid-i-Azam University, Pakistan, 1987.
[11]	M. A. Kazim, M. Naseeruddin, On almost semigroups, Port. Math., 2 (1972), 1–7.
[12]	M. Khan, F. Yousafzai, On fuzzy ordered Abel-Grassmann's groupoids, J. Math. Res., 3 (2011), 27–40. https://doi.org/10.5539/jmr.v3n2p27 doi: 10.5539/jmr.v3n2p27
[13]	M. Khan, Y. B. Jun, F. Yousafzai, Fuzzy ideals in right regular left almost semigroups, Hacet. J. Math. Stat., 44 (2015), 569–586.
[14]	S. Lajos, A note on completely regular remigroups, Acta Sci. Math. Szeged, 28 (1967), 261–265.
[15]	Q. Mushtaq, S. M. Yusuf, On LA-semigroups, Alig. Bull. Math., 8 (1978), 65–70.
[16]	M. Riaz, M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, J. Intel. Fuzzy Syst., 37 (2019), 5417–5439. https://doi.org/10.3233/JIFS-190550 doi: 10.3233/JIFS-190550
[17]	T. Saito, On semigroups which are semilattices of left simple semigroups, Math. Japon, 18 (1973), 95–97.
[18]	N. Stevanović, P. V. Protić, Composition of Abel-Grassmann's 3-bands, Novi Sad J. Math., 34 (2004), 175–182.
[19]	J. P. Xu, F. Shen, A new outranking choice method for group decision making under Atanassov's interval-valued intuitionistic fuzzy environment, Knowl-Based Syst., 70 (2014), 177–188. https://doi.org/10.1016/j.knosys.2014.06.023 doi: 10.1016/j.knosys.2014.06.023
[20]	S. Z. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control Decis., 22 (2007), 215–219.
[21]	R. P. Yager, Pythagorean fuzzy subsets, In Proceedings of the IFSA World Congress and NAFIPS Annual Meeting, Edmonton, AB, Canada, 2013, 57–61.
[22]	R. P. Yager, Generalized orthopair fuzzy sets, IEEE T. Fuzzy Syst., 25 (2017), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
[23]	F. Yousafzai, N. Yaqoob, A. Ghareeb, Left regular $\mathcal{AG}$-groupoids in terms of fuzzy interior ideals, Afr. Math., 24 (2013), 577–587.
[24]	F. Yousafzai, N. Yaqoob, K. Hila, On fuzzy (2, 2)-regular ordered $\Gamma$ -AG*-groupoids, UPB Sci. Bull. Ser. A*, 74 (2012), 87–104.
[25]	F. Yousafzai, A. Khan, V. Amjad, A. Zeb, On fuzzy fully regular ordered AG-groupoids, J. Intell. Fuzzy Syst., 26 (2014), 2973–2982. https://doi.org/10.3233/IFS-130963 doi: 10.3233/IFS-130963
[26]	F. Yousafzai, M. Khan, B. Davvaz, S. Haq, A note on fuzzy ordered AG-groupoids, J. Intell. Fuzzy Syst., 26 (2014), 2251–2261.
[27]	F. Yousafzai, N. Yaqoob, A. Zeb, On generalized fuzzy ideals of ordered AG-groupoids, Int. J. Mach. Learn. Cyb., 7 (2016), 995–1004.
[28]	F. Yousafzai, M. M. Khalaf, A. Ali, A. B. Saeid, Non-associative ordered semigroups based on soft sets, Commun. Algebra, 47 (2019), 312–327. https://doi.org/10.1080/00927872.2018.1476524 doi: 10.1080/00927872.2018.1476524
[29]	Z. L. Yue, Y. Y. Jia, A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making, Appl. Soft Comput., 13 (2013), 2304–2317. https://doi.org/10.1016/j.asoc.2012.12.032 doi: 10.1016/j.asoc.2012.12.032
[30]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)