On Min-Max Goal Programming Approach for Solving Piecewise Quadratic Fuzzy Multi- Objective De Novo Programming Problems

Authors

  • Hamiden Abd El- Wahed Khalifa Department of Operations Research, Graduate School for Statistical Research, Cairo University, Giza, Egypt Author
  • S. A. Edalatpanah Department of Applied Mathematics, Ayendang Institute of Higher Education, Tonkabon, Iran Author
  • Darko Bozanic University of Defense in Belgrade, Serbia Author

DOI:

https://doi.org/10.31181/sa21202411

Keywords:

Multi-objective de novo programming, Piecewise quadratic fuzzy numbers, Close interval approximation, α-Fuzzy efficient, Goal programming, Optimal system design, Parametric study

Abstract

De novo programming is considered an essential tool for establishing optimal system design. This paper studies the Multi-Objective De Novo Programming (MODNP) problem with Piecewise Quadratic Fuzzy (PQF) data in the objective function coefficients. One of the best interval approximations, namely, the close interval approximation of the PQF number, is applied to solve the MODNP problem. A necessary and sufficient condition for the solution from the efficiency standpoint is established. A Min-max goal programming approach with positive and negative ideals is proposed to obtain optimal compromise system design. The stability set of the first kind corresponding to the optimal system design is defined and determined. The stability set of the first kind corresponding to the optimal system design is determined. The steps of the proposed solution approach are illustrated through numerical examples.

References

Hwang, C. L., Paidy, S. R., Masud, A. S. M., & Yoon, K. (2012). Multiple objective decision making — methods and applications: a state-of-the-art survey. Springer Berlin Heidelberg. https://books.google.com/books?id=M0noCAAAQBAJ

Wang, S., & Chiang, H. D. (2019). Constrained multiobjective nonlinear optimization: a user preference enabling method. IEEE transactions on cybernetics, 49(7), 2779–2791. DOI:10.1109/TCYB.2018.2833281

Kundu, T., & Islam, S. (2019). An interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem. Journal of industrial engineering international, 15(1), 95–104. https://doi.org/10.1007/s40092-019-0321-y

Waliv, R. H., Mishra, U., Garg, H., & Umap, H. P. (2020). A nonlinear programming approach to solve the stochastic multi-objective inventory model using the uncertain information. Arabian journal for science and engineering, 45(8), 6963–6973. https://doi.org/10.1007/s13369-020-04618-z

Ahmad, F. (2021). Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems. Complex & intelligent systems, 7(4), 1935–1954. https://doi.org/10.1007/s40747-021-00299-9

Liu, X., Liu, Y., He, X., Xiao, M., & Jiang, T. (2021). Multi-objective nonlinear programming model for reducing octane number loss in gasoline refining process based on data mining technology. Processes, 9(4), 1–19. https://www.mdpi.com/2227-9717/9/4/721

Zeleny, M. (2012). Multiple criteria decision making kyoto 1975. Springer Berlin Heidelberg. https://books.google.com/books?id=kUrmCAAAQBAJ

Zeleny, M. (1986). Optimal system design with multiple criteria: de novo programming approach. Engineering costs and production economics, 10(1), 89–94. https://www.sciencedirect.com/science/article/pii/0167188X86900297

Zelený, M. (1990). Optimizing given systems vs. designing optimal systems: the de novo programming approach. International journal of general systems, 17(4), 295–307. https://doi.org/10.1080/03081079008935113

Shi, Y. (1999). Optimal system design with multiple decision makers and possible debt: a multicriteria de novo programming approach. Operations research, 47(5), 723–729. https://doi.org/10.1287/opre.47.5.723

Zhang, Y. M., Huang, G. H., & Zhang, X. D. (2009). Inexact de novo programming for water resources systems planning. European journal of operational research, 199(2), 531–541. https://www.sciencedirect.com/science/article/pii/S0377221708010060

Chen, J. K. C., & Tzeng, G. H. (2009). Perspective strategic alliances and resource allocation in supply chain systems through the de novo programming approach. International journal of sustainable strategic management, 1(3), 320–339. https://www.inderscienceonline.com/doi/abs/10.1504/IJSSM.2009.026285

Umarusman, N. (2013). Min-max goal programming approach for solving multi-objective de novo programming problems. International journal of operations research, 10(2), 92–99. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=4dd384b06495c580c325ef9d262fb86266d655cb

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://www.sciencedirect.com/science/article/pii/S001999586590241X

Dubois, D. J. (1980). Fuzzy sets and systems: theory and applications. Elsevier Science. https://books.google.com/books?id=JmjfHUUtMkMC

Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), 1–141. https://doi.org/10.1287/mnsc.17.4.B141

Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45–55. https://www.sciencedirect.com/science/article/pii/0165011478900313

Chen, Y. W., & Hsieh, H. E. (2006). Fuzzy multi-stage de-novo programming problem. Applied mathematics and computation, 181(2), 1139–1147. https://www.sciencedirect.com/science/article/pii/S0096300306001986

J-J Huang, G. H. T., & Ong, C. S. (2006). Choosing best alliance partners and allocating optimal alliance resources using the fuzzy multi-objective dummy programming model. Journal of the operational research society, 57(10), 1216–1223. https://doi.org/10.1057/palgrave.jors.2602108

Charnes, A., & Cooper, W. W. (1957). Management models and industrial applications of linear programming. Management science, 4(1), 38–91. https://doi.org/10.1287/mnsc.4.1.38

Lee, S. M. (1972). Goal programming for decision analysis. Auerbach Publishers. https://cir.nii.ac.jp/crid/1130000794581506944

Ijiri, Y. (1965). Management goals and accounting for control. North Holland Publishing Company. https://books.google.com/books?id=KCkUAQAAMAAJ

Ignizio, J. P. (1982). Linear programming in single- multiple-objective systems. Prentice-Hall. https://cir.nii.ac.jp/crid/1130282271612104960

Jones, D., Tamiz, M., & others. (2010). Practical goal programming (Vol. 141). Springer. https://link.springer.com/content/pdf/10.1007/978-1-4419-5771-9.pdf

Osman, M. S. A. (1977). Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints. Aplikace matematiky, 22(5), 318–332. https://dml.cz/dmlcz/103710

Osman, M. S., & El-Banna, A. Z. H. (1993). Stability of multiobjective nonlinear programming problems with fuzzy parameters. Mathematics and computers in simulation, 35(4), 321–326. https://www.sciencedirect.com/science/article/pii/037847549390062Y

Jain, S. (2010). Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program. Iranian journal of operations research, 2(1), 77–88. https://www.sid.ir/EN/VEWSSID/J_pdf/115720100106.pdf

Chankong, V., & Haimes, Y. Y. (2008). Multiobjective decision making: theory and methodology. Dover Publications. https://books.google.com/books?id=o371DAAAQBAJ

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Published

2024-02-29

Data Availability Statement

All data supporting the reported findings in this research paper are provided within the manuscript.

Issue

Vol. 2 No. 1 (2024): Systemic Analytics

Section

Articles

How to Cite

Abd El- Wahed Khalifa, H., Edalatpanah, S. A., & Bozanic, D. (2024). On Min-Max Goal Programming Approach for Solving Piecewise Quadratic Fuzzy Multi- Objective De Novo Programming Problems. Systemic Analytics, 2(1), 35-47. https://doi.org/10.31181/sa21202411