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.
Similar content being viewed by others
References
Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)
Fuller, R.: Fuzzy Reasoning and Fuzzy Optimization. Turku Centre for Computer Science (1998)
Abo-Sinna, M.A.: A bi-level non-linear multi-objective decision making under fuzziness. OPSEARCH 38(5), 484–495 (2001)
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)
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)
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)
Lu, J., Han, J., Hu, Y., Zhang, G.: Multilevel decision-making: a survey. Inf Sci 346, 463–487 (2016)
Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: a bibliography review. J. Global Optim. 5, 291–306 (1994)
Baron, D.P.: Quadratic programming with quadratic constraints. Naval Res Logist. Q. 19(2), 253–260 (1972)
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)
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)
Kumar, A., Kaur, J., Singh, P.: A new method for solving fully fuzzy linear programming problems. Appl. Math. Model. 35, 817–823 (2011)
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)
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)
Ren, A.: A novel method for solving the fully fuzzy bilevel linear programming problem. Math. Probl. Eng. 2015(2), 1–11 (2015)
Lachhwani, K.: On solving multi-level multi objective linear programming problems through fuzzy goal programming approach. OPSEARCH 51(4), 624–637 (2014)
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)
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)
Ranarahu, N., Dash, J.K., Acharya, S.: Multi-objective bilevel fuzzy probabilistic programming problem. OPSEARCH 54(3), 475–504 (2017)
Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
AbdAlhakim, H., Emam, O.E. & Abd El-Mageed, A.A. Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem. OPSEARCH 56, 367–389 (2019). https://doi.org/10.1007/s12597-019-00368-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-019-00368-1