A Multi-Level Multi-Objective Integer Quadratic Programming Problem Under Pentagonal Neutrosophic Environment

N. M. Bekhit; O. E. Emam; Laila Abd Elhamid

doi:10.26599/FIE.2023.9270025

Fuzzy Information and Engineering 2023, 15(4): 347-361 https://doi.org/10.26599/FIE.2023.9270025

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Open Access | Issue | Published: 02 January 2024

A Multi-Level Multi-Objective Integer Quadratic Programming Problem Under Pentagonal Neutrosophic Environment

Show Author's Information Hide Author's Information N. M. Bekhit^{¹^,²}(

), O. E. Emam^², Laila Abd Elhamid^²

1Information Systems Department, Faculty of Computers and Artificial Intelligence, South Valley University, Hurghada 84511, Egypt

2Information Systems Department, Faculty of Computers and Artificial Intelligence, Helwan University, Cairo 11795, Egypt

Keywords:

fuzzy approach, integer programming, quadratic programming, Pentagonal Neutrosophic numbers, multi-level multi-objective programming, branch and bound method, score and accuracy function

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Bekhit NM, Emam OE, Elhamid LA. A Multi-Level Multi-Objective Integer Quadratic Programming Problem Under Pentagonal Neutrosophic Environment. Fuzzy Information and Engineering, 2023, 15(4): 347-361. https://doi.org/10.26599/FIE.2023.9270025

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Abstract

The aim of this paper is to propose an algorithm to solve and enhance a multi-level multi-objective integer quadratic programming problem (MLMOIQPP) under a single-valued Pentagonal Neutrosophic environment applied to the objective functions. The suggested solution takes advantage of multi-objective optimization in addition to the fuzzy approach as well as the branch and bound technique, which is implemented at each decision level to develop a generalized maximization-minimization model for obtaining the integer satisfactory solution after applying the score and accuracy function in the first phase of the solution methodology to single-valued Pentagonal Neutrosophic parameters to be converted into an equal crisp form. An illustrative example is demonstrated to validate the proposed solution algorithm.

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A Multi-Level Multi-Objective Integer Quadratic Programming Problem Under Pentagonal Neutrosophic Environment

Show Author's information Hide Author's Information N. M. Bekhit^{¹^,²}(

), O. E. Emam^², Laila Abd Elhamid^²

1Information Systems Department, Faculty of Computers and Artificial Intelligence, South Valley University, Hurghada 84511, Egypt

2Information Systems Department, Faculty of Computers and Artificial Intelligence, Helwan University, Cairo 11795, Egypt

Abstract

Keywords: fuzzy approach, integer programming, quadratic programming, Pentagonal Neutrosophic numbers, multi-level multi-objective programming, branch and bound method, score and accuracy function

References(30)

[1]

L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.

DOI Google Scholar

[2]

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96, 1986.

DOI Google Scholar

[3]

O. E. Emam, A. Abdo, and A. M. Youssef, Solving bi-level multi-objective quadratic programming problem with neutrosophic parameters in objective functions and constraints using fuzzy approach, J. Stat. Appl. Probab., vol. 11, no. 2, pp. 581–590, 2022.

DOI Google Scholar

[4]

F. Smarandache, A Unifying Field in Logics : Neutrosophic Logic. Rehoboth, DE, USA: American Research Press, 1999.

[5]

S. Broumi, A. Bakali, M. Talea, F. Smarandache, V. Uluçay, M. Sahin, A. Dey, M. Dhar, R. P. Tan, A. Bahnasse, et al., Neutrosophic sets: An overview, in New Trends in Neutrosophic Theory and Applications, F. Smarandache and S. Pramanik, eds. Brussels, Belgium: Pons Edition, 2018, pp. 389−419.

[6]

H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, Single valued neutrosophic sets, in Multispace & Multistructure Neutrosophic Transdisciplinarity, F. Smarandache, ed. Hanko, Finland: North-European Scientific Publishers, 2010, pp. 410−413.

[7]

F. Smarandache, n-valued refined neutrosophic logic and its applications to physics, arXiv preprint arXiv: 1407.1041, 2014.

[8]

A. Chakraborty, S. Broumi, and P. K. Singh, Some properties of Pentagonal Neutrosophic numbers and its applications in transportation problem environment, Neutrosophic Sets Syst., vol. 28, p. 16, 2019.

Google Scholar

[9]

A. Chakraborty, S. Mondal, and S. Broumi, De-neutrosophication technique of Pentagonal Neutrosophic number and application in minimal spanning tree, Neutrosophic Sets Syst., vol. 29, p. 1, 2019.

Google Scholar

[10]

A. Chakraborty, A new score function of Pentagonal Neutrosophic number and its application in networking problem, Int. J. Neutrosophic Sci., vol. 1, no. 1, pp. 40–51, 2020.

DOI Google Scholar

[11]

K. Radhika and K. A. Prakash, Ranking of Pentagonal Neutrosophic numbers and its applications in assignment problem, Neutrosophic Sets Syst., vol. 35, no. 1, pp. 464−477, 2020.

Google Scholar

[12]

M. S. Osman, M. A. Abo-Sinna, A. H. Amer, and O. E. Emam, A multi-level non-linear multi-objective decision-making under fuzziness, Appl. Math. Comput., vol. 153, no. 1, pp. 239–252, 2004.

DOI Google Scholar

[13]

U. Emam, A multi-level multi-objective quadratic programming problem with fuzzy parameters on objective functions, Int. J. Comput. Technol., vol. 15, no. 5, pp. 6738–6748, 2016.

DOI Google Scholar

[14]

O. E. Emam, M. A. Abdel-Fattah, and S. M. Azzam, A fuzzy approach for solving a three-level linear programming problem with neutrosophic parameters in the objective functions and constraints, J. Stat. Appl. Probab., vol. 10, no. 3, pp. 677–686, 2021.

DOI Google Scholar

[15]

S. Luo, W. Pedrycz, and L. Xing, Interactive multilevel programming approaches in neutrosophic environments, J. Ambient Intell. Humaniz. Comput., vol. 13, no. 4, pp. 2143–2159, 2022.

DOI Google Scholar

[16]

J. H. Cho, Y. Wang, I. R. Chen, K. S. Chan, and A. Swami, A survey on modeling and optimizing multi-objective systems, IEEE Commun. Surv. Tutor., vol. 19, no. 3, pp. 1867–1901, 2017.

DOI Google Scholar

[17]

S. Khalil, S. Kousar, G. Freen, and M. Imran, Multi-objective interval-valued neutrosophic optimization with application, Int. J. Fuzzy Syst., vol. 24, no. 3, pp. 1343–1355, 2022.

DOI Google Scholar

[18]

M. Lapucci and P. Mansueto, A limited memory Quasi-Newton approach for multi-objective optimization, Comput. Optim. Appl., vol. 85, no. 1, pp. 33–73, 2023.

DOI Google Scholar

[19]

E. K. Lee and J. E. Mitchell, Integer programming: Branch and bound methods, in Encyclopedia of Optimization, C. A. Floudas and P. M. Pardalos, eds. Boston, MA, USA: Springer, 2008, pp. 1634–1643.

DOI

[20]

B. W. Taylor, Module C: Integer programming: The branch and bound method, in Introduction to Management Science, https://repository.dinus.ac.id/docs/ajar/01._Bernard_W_._Taylor_Introduction_to_Management_Science_11th_2013_.pdf, 2013.

[21]

S. Liu, M. Wang, N. Kong, and X. Hu, An enhanced branch-and-bound algorithm for bilevel integer linear programming, Eur. J. Oper. Res., vol. 291, no. 2, pp. 661–679, 2021.

DOI Google Scholar

[22]

N. Forget, S. L. Gadegaard, K. Klamroth, L. R. Nielsen, and A. Przybylski, Branch-and-bound and objective branching with three or more objectives, Comput. Oper. Res., vol. 148, p. 106012, 2022.

DOI Google Scholar

[23]

N. Forget, S. L. Gadegaard, and L. R. Nielsen, Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs, Eur. J. Oper. Res., vol. 302, no. 3, p. 909–924, 2022.

DOI Google Scholar

[24]

S. Broumi, D. Ajay, P. Chellamani, L. Malayalan, M. Talea, A. Bakali, P. Schweizer, and S. Jafari, Interval valued pentapartitioned neutrosophic graphs with an application to MCDM, Oper. Res. Eng. Sci. Theor. Appl., vol. 5, no. 3, pp. 68–91, 2022.

DOI Google Scholar

[25]

S. K. Das and A. Chakraborty, A new approach to evaluate linear programming problem in Pentagonal Neutrosophic environment, Complex Intell. Syst., vol. 7, no. 1, pp. 101–110, 2021.

DOI Google Scholar

[26]

A. H. Amer and M. A. Abo-Sinna, A new approach for solving bi-level multi-objective nonlinear programming model under neutrosophic environment, Neutrosophic Sets and Systems, vol. 47, no. 1, pp. 224–239, 2021.

Google Scholar

[27]

M. Abdel-Baset, M. Mohamed, A. N. Hessian, and F. Smarandache, Neutrosophic integer programming problems, Neutrosophic Oper. Res., vol. 1, pp. 49–61, 2018.

Google Scholar

[28]

A. H. Nafei and S. H. Nasseri, A new approach for solving neutrosophic integer programming problems, https://www.researchgate.net/publication/336511455, 2019.

[29]

O. E. Emam, A fuzzy approach for bi-level integer non-linear programming problem, Appl. Math. Comput., vol. 172, no. 1, pp. 62–71, 2006.

DOI Google Scholar

[30]

J. Ye, Trapezoidal neutrosophic set and its application to multiple attribute decision-making, Neural Comput. Appl., vol. 26, no. 5, pp. 1157–1166, 2015.

DOI Google Scholar

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Received: 22 June 2023

Revised: 04 August 2023

Accepted: 15 August 2023

Published: 02 January 2024

Issue date: December 2023

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).