no. 1
A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator
RAIRO. Operations Research, Tome 56 (2022) no. 1, pp. 275-292

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2022006
Classification : 03B52, 03F55, 62J05, 62J99
Keywords: Decision-making problem, multi-objective optimization problem, hesitant fuzzy membership function, hesitant fuzzy aggregation operator 
@article{RO_2022__56_1_275_0,
     author = {Ahmad, Firoz and Adhami, Ahmad Yusuf and John, Boby and Reza, Amit},
     title = {A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator},
     journal = {RAIRO. Operations Research},
     pages = {275--292},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {1},
     doi = {10.1051/ro/2022006},
     mrnumber = {4376294},
     zbl = {1480.91081},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2022006/}
}
TY  - JOUR
AU  - Ahmad, Firoz
AU  - Adhami, Ahmad Yusuf
AU  - John, Boby
AU  - Reza, Amit
TI  - A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator
JO  - RAIRO. Operations Research
PY  - 2022
SP  - 275
EP  - 292
VL  - 56
IS  - 1
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2022006/
DO  - 10.1051/ro/2022006
LA  - en
ID  - RO_2022__56_1_275_0
ER  - 
%0 Journal Article
%A Ahmad, Firoz
%A Adhami, Ahmad Yusuf
%A John, Boby
%A Reza, Amit
%T A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator
%J RAIRO. Operations Research
%D 2022
%P 275-292
%V 56
%N 1
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2022006/
%R 10.1051/ro/2022006
%G en
%F RO_2022__56_1_275_0
Ahmad, Firoz; Adhami, Ahmad Yusuf; John, Boby; Reza, Amit. A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator. RAIRO. Operations Research, Tome 56 (2022) no. 1, pp. 275-292. doi: 10.1051/ro/2022006

[1] A. Y. Adhami and F. Ahmad, Interactive pythagorean-hesitant fuzzy computational algorithm for multiobjective transportation problem under uncertainty. Int. J. Manage. Sci. Eng. Manage. 15 (2020) 288–297.

[2] A. Y. Adhami, F. Ahmad and N. Wani, Overall shale gas water management a neutrosophic optimization approach. In: Optimal Decision Making in Operations Research and Statistics: Methodologies and Applications. CRC Press (2021) 321. | MR | DOI

[3] F. Ahmad, Interactive neutrosophic optimization technique for multiobjective programming problems: an application to pharmaceutical supply chain management. Annals of Operations Research (2021) 1–35. DOI: . | DOI | MR

[4] F. Ahmad, Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems. Complex Intell. Syst. 7 (2021) 1935–1954. | DOI

[5] F. Ahmad and A. Y. Adhami, Neutrosophic programming approach to multiobjective nonlinear transportation problem with fuzzy parameters. Int. J. Manage. Sci. Eng. Manage. 14 (2019) 218–229.

[6] F. Ahmad and B. John, A fuzzy quantitative model for assessing the performance of pharmaceutical supply chain under uncertainty. Kybernetes (2021). DOI: . | DOI

[7] F. Ahmad and F. Smarandache, Neutrosophic fuzzy goal programming algorithm for multi-level multiobjective linear programming problems. Neutrosophic Operational Research, Springer (2021) 593–61. | DOI

[8] F. Ahmad, A. Y. Adhami and F. Smarandache, Single valued neutrosophic hesitant fuzzy computational algorithm for multiobjective nonlinear optimization problem. Neutrosophic Sets Syst. 22 (2018) 76–86.

[9] F. Ahmad, A. Y. Adhami and F. Smarandache, Neutrosophic optimization model and computational algorithm for optimal shale gas water management under uncertainty. Symmetry 11 (2019) 544. | DOI

[10] F. Ahmad, S. Ahmad, A. T. Soliman and M. Abdollahian, Solving multi-level multiobjective fractional programming problem with rough interval parameter in neutrosophic environment. RAIRO-Oper. Res. 55 (2021) 2567–2581. | MR | Numdam | DOI

[11] F. Ahmad, S. Ahmad and M. Zaindin, A sustainable production and waste management policies for covid-19 medical equipment under uncertainty: a case study analysis. Comput. Ind. Eng. 157 (2021) 107381. | DOI

[12] F. Ahmad, S. Ahmad, M. Zaindin and A. Y. Adhami, A robust neutrosophic modeling and optimization approach for integrated energy-food-water security nexus management under uncertainty. Water 13 (2021) 121. | DOI

[13] F. Ahmad, K. A. Alnowibet, A. F. Alrasheedi and A. Y. Adhami, A multi-objective model for optimizing the socio-economic performance of a pharmaceutical supply chain. Soc.-Econ. Planning Sci. 79 (2021) 101126. | DOI

[14] S. Ahmad, F. Ahmad and M. Sharaf, Supplier selection problem with type-2 fuzzy parameters: a neutrosophic optimization approach. Int. J. Fuzzy Syst. 23 (2021) 755–775. | DOI

[15] A. A. H. Ahmadini and F. Ahmad, A novel intuitionistic fuzzy preference relations for multiobjective goal programming problems. J. Intell. Fuzzy Syst. 40 (2021) 4761–4777.

[16] A. A. H. Ahmadini and F. Ahmad, Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment. AIMS Math. 6 (2021) 4556–4580. | MR | DOI

[17] R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment. Manage. Sci. 17 (1970) B-141–B-164. | MR | Zbl | DOI

[18] S. K. Bharati, Hesitant fuzzy computational algorithm for multiobjective optimization problems. Int. J. Dyn. Control 6 (2018) 1799–1806. | MR | DOI

[19] A. Biswas and N. Modak, A multiobjective fuzzy chance constrained programming model for land allocation in agricultural sector: a case study. Int. J. Comput. Intell. Syst. 10 (2017) 196–211. | DOI

[20] H. Cheng, W. Huang, Q. Zhou and J. Cai, Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method. Appl. Math. Modell. 37 (2013) 6855–6869. | MR | Zbl | DOI

[21] E. D. Dolan, The neos server 4.0 administrative guide. Technical Memorandum ANL/MCS-TM-250, Mathematics and Computer Science Division, Argonne National Laboratory (2001). | DOI

[22] L. Li and K. K. Lai, A fuzzy approach to the multiobjective transportation problem. Comput. Oper. Res. 27 (2000) 43–57. | MR | Zbl | DOI

[23] S. Liu, Z. Xu and J. Gao, A fuzzy compromise programming model based on the modified s-curve membership functions for supplier selection. Granular Comput. 3 (2018) 275–283. | DOI

[24] S. K. Singh and S. P. Yadav, Modeling and optimization of multi objective non-linear programming problem in intuitionistic fuzzy environment. Appl. Math. Model. 39 (2015) 4617–4629. | MR | Zbl | DOI

[25] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision. In: 2009 IEEE International Conference on Fuzzy Systems. IEEE (2009) 1378–1382. | DOI

[26] S.-P. Wan, Y.-L. Qin and J.-Y. Dong, A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees. Knowl.-Based Syst. 138 (2017) 232–248. | DOI

[27] S.-P. Wan, Z. Jin and J.-Y. Dong, Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with pythagorean fuzzy truth degrees. Knowl. Inf. Syst. 55 (2018) 437–466. | DOI

[28] S.-P. Wan, W.-C. Zou, L.-G. Zhong and J.-Y. Dong, Some new information measures for hesitant fuzzy promethee method and application to green supplier selection. Soft Comput. 24 (2020) 9179–9203. | Zbl | DOI

[29] M. Xia and Z. Xu, Hesitant fuzzy information aggregation in decision making. Int. J. Approximate Reasoning 52 (2011) 395–407. | MR | Zbl | DOI

[30] M. Xia, Z. Xu and N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negotiation 22 (2013) 259–279. | DOI

[31] G.-L. Xu, S.-P. Wan and J.-Y. Dong, A hesitant fuzzy programming method for hybrid madm with incomplete attribute weight information. Informatica 27 (2016) 863–892. | Zbl | DOI

[32] J. Ye, Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. J. Intell. Syst. 24 (2015) 23–36.

[33] M. Zangiabadi and H. R. Maleki, Fuzzy goal programming technique to solve multiobjective transportation problems with some non-linear membership functions. Iran. J. Fuzzy Syst. 10 (2013) 61–74. | MR | Zbl

[34] S. Zhang, C. Ka, M. Lee, K. Wu and K. Lun, Multi-objective optimization for sustainable supply chain network design considering multiple distribution channels. Expert Syst. Appl. 65 (2016) 87–99. | DOI

[35] X. Zhang, Z. Xu and X. Xing, Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences. OR Spectr. 38 (2016) 789–817. | MR | Zbl | DOI

[36] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1 (1978) 45–55. | MR | Zbl | DOI

Cité par Sources :