Advertisement

OPSEARCH

pp 1–23 | Cite as

Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem

  • Hawaf AbdAlhakim
  • O. E. Emam
  • A. A. Abd El-MageedEmail author
Theoretical Article
  • 98 Downloads

Abstract

Fully fuzzy quadratic programming became emerge naturally in numerous real-world applications. Therefore, an effective model based on the bound and decomposition method and the separable programming method is proposed in this paper for solving Fully Fuzzy Multi-Level Quadratically Constrained Quadratic Programming (FFMLQCQP) problem, where the objective function and the constraints are quadratic, also all the coefficients and variables of both objective functions and constraints are described fuzzily as fuzzy numbers. The bound and decomposition method is recommended to decompose the given (FFMLQCQP) problem into series of crisp Quadratically Constrained Quadratic Programming (QCQP) problems with bounded variable constraints for each level. Each (QCQP) problem is then solved independently by utilizing the separable programming method, which replaces the quadratic separable functions with linear functions. At last, the fuzzy optimal solution to the given (FFMLQCQP) problem is obtained. The effectiveness of the proposed model is illustrated through an illustrative numerical example.

Keywords

Fully fuzzy programming Multi-level programming Quadratic programming Bound and decomposition method Separable programming method 

Notes

References

  1. 1.
    Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)CrossRefGoogle Scholar
  2. 2.
    Fuller, R.: Fuzzy Reasoning and Fuzzy Optimization. Turku Centre for Computer Science (1998)Google Scholar
  3. 3.
    Abo-Sinna, M.A.: A bi-level non-linear multi-objective decision making under fuzziness. OPSEARCH 38(5), 484–495 (2001)CrossRefGoogle Scholar
  4. 4.
    Khan, I.U., Ahmad, T., Maan, N.: A simplified novel technique for solving fully fuzzy linear programming problems. J Optim Theory Appl 159(2), 536–546 (2013)CrossRefGoogle Scholar
  5. 5.
    Nasseri, S.H., Behmanesh, E., Taleshian, F., Abdolalipoor, M., Taghi-Nezhad, N.A.: Fully fuzzy linear programming with inequality constraints. Int J Ind Math 5(4), 309–316 (2013)Google Scholar
  6. 6.
    Dhurai, K., Karpagam, A.: A new pivotal operation on triangular fuzzy number for solving fully fuzzy linear programming problems. Int J Appl Math Sci 9(1), 41–46 (2016)Google Scholar
  7. 7.
    Lu, J., Han, J., Hu, Y., Zhang, G.: Multilevel decision-making: a survey. Inf Sci 346, 463–487 (2016)CrossRefGoogle Scholar
  8. 8.
    Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: a bibliography review. J. Global Optim. 5, 291–306 (1994)CrossRefGoogle Scholar
  9. 9.
    Baron, D.P.: Quadratic programming with quadratic constraints. Naval Res Logist. Q. 19(2), 253–260 (1972)CrossRefGoogle Scholar
  10. 10.
    Lu, C., Fang, S., Jin, Q., Wang, Z., Xing, W.: KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems. Soc. Ind. Appl. Math. 21(4), 1475–1490 (2011)Google Scholar
  11. 11.
    Bose, S., Gayme, D.F., Chandy, K.M.: Quadratically constrained quadratic programs on acyclic graphs with application to power flow. IEEE Trans. Control Netw. Syst. 2(3), 278–287 (2015)CrossRefGoogle Scholar
  12. 12.
    Kumar, A., Kaur, J., Singh, P.: A new method for solving fully fuzzy linear programming problems. Appl. Math. Model. 35, 817–823 (2011)CrossRefGoogle Scholar
  13. 13.
    Allahviranloo, T., Lotfi, F.H., Kiasary, M.K., Kiani, N.A., Alizadeh, L.: Solving fully fuzzy linear programming problem by the ranking function. Appl. Math. Sci. 2(1), 19–32 (2008)Google Scholar
  14. 14.
    Ezzati, R., Khorram, E., Enayati, R.: A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Appl. Math. Model. 39(12), 3183–3193 (2015)CrossRefGoogle Scholar
  15. 15.
    Ren, A.: A novel method for solving the fully fuzzy bilevel linear programming problem. Math. Probl. Eng. 2015(2), 1–11 (2015)Google Scholar
  16. 16.
    Lachhwani, K.: On solving multi-level multi objective linear programming problems through fuzzy goal programming approach. OPSEARCH 51(4), 624–637 (2014)CrossRefGoogle Scholar
  17. 17.
    Youness, E.A., Emam, O.E., Hafez, M.S.: Fuzzy bi-level multi-objective fractional integer programming. Appl. Math. Inf. Sci. 8(6), 2857–2863 (2014)CrossRefGoogle Scholar
  18. 18.
    Osman, M.S., Emam, O.E., El Sayed, M.A.: Stochastic fuzzy multi-level multi-objective fractional programming problem: a FGP approach. OPSEARCH 54(2), 816–840 (2017)CrossRefGoogle Scholar
  19. 19.
    Ranarahu, N., Dash, J.K., Acharya, S.: Multi-objective bilevel fuzzy probabilistic programming problem. OPSEARCH 54(3), 475–504 (2017)CrossRefGoogle Scholar
  20. 20.
    Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York (1985)Google Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  • Hawaf AbdAlhakim
    • 1
  • O. E. Emam
    • 1
  • A. A. Abd El-Mageed
    • 1
    Email author
  1. 1.Faculty of Computers and Information, Information Systems DepartmentHelwan UniversityCairoEgypt

Personalised recommendations