A Goal Programming Approach to Solve Multi-objective Chance Constrained Programming in Fuzzy Environment





Multi objective fuzzy chance constrained nonlinear programming problem, MOFCCNLPP, Trapezoidal fuzzy numbers, Rayleigh distribution, Goal programming


A new solution process is presented to solve multi-objective fuzzy chance constrained nonlinear decision making problems using goal programming techniques. The right sided parameters of probabilistic constraints are assumed to follow Rayleigh distribution with known parameters whereas the constraints coefficients are trapezoidal fuzzy numbers. The stochastic constraints are transformed into fuzzy constraints using CCP technique and \(\alpha\)-cut techniques are applied to obtain the identical crisp nonlinear programming problem. The crisp MONLPP is solved by goal programming by means of membership and non-membership functions. The proposed solution methodology is validated by an example.


Download data is not yet available.


S. K. Barik, Probabilistic fuzzy goal programming problems involving pareto distribution: some additive approaches, Fuzzy Information and Engineering 7(2) (2015), 227 – 244, DOI: 10.1016/j.fiae.2015.05.007.

S. K. Barik and M. P. Biswal, Probabilistic quadratic programming problems with some fuzzy parameters, Advances in Operations Research 2012 (2012), Article ID 635282, DOI: 10.1155/2012/635282.

M. P. Biswal and S. Acharya, Multi-choice multi-objective linear programming problem, Journal of Interdisciplinary Mathematics 12(5) (2009), 606 – 637, DOI: 10.1080/09720502.2009.10700650.

A. Biswas and N. Modak, Using fuzzy goal programming technique to solve multiobjective chance constrained programming problems in a fuzzy environment, International Journal of Fuzzy System Applications 2(1) (2012), 71 – 80, DOI: 10.4018/IJFSA.2012010105.

H. Dalman and M. Bayram, interactive fuzzy goal programming based on taylor series to solve multiobjective nonlinear programming problems with interval type-2 fuzzy numbers, IEEE Transactions on Fuzzy Systems 26(4) (2018), 2434 – 2449, DOI: 10.1109/TFUZZ.2017.2774191.

H. A. El-Wahed Khalifa, P. Kumar and S. S. Alodhaibi, Stochastic multi-objective programming problem: a two-phase weighted coefficient approach, Mathematical Modelling of Engineering Problems 8(6) (2021), 854 – 860, DOI: 10.18280/mmep.080603.

H. A. Khalifa, On solutions of possibilistic multi-objective quadratic programming problems, International Journal of Supply and Operations Management 4(2) (2017), 150 – 157, URL: http://www.ijsom.com/article_2728_61dedbc786adb8107bbd87fae493239c.pdf.

M. Masoud, H. A. Khalifa, S. Q. Liu, M. Elhenawy and P. Wu, A fuzzy goal programming approach for solving fuzzy multi-objective stochastic linear programming problem, 2019 International Conference on Industrial Engineering and Systems Management (IESM), Shanghai, China, 2019, pp. 1 – 6, DOI: 10.1109/IESM45758.2019.8948204.

P. K. Rout, S. Nanda and S. Acharya, Multi-objective fuzzy probabilistic quadratic programming problem, International Journal of Operational Research 34(3) (2019), 387 – 408, DOI: https://dx.doi.org/10.1504/IJOR.2019.10019738.




How to Cite

Beaula, T., & Seetha, R. (2023). A Goal Programming Approach to Solve Multi-objective Chance Constrained Programming in Fuzzy Environment. Communications in Mathematics and Applications, 14(1), 203–213. https://doi.org/10.26713/cma.v14i1.2040



Research Article