In this paper, an interactive approach for solving multi-level multi-objective fractional programming (ML-MOFP) problem under hybrid uncertainty is developed. The proposed interactive approach makes an extension work of Shi and Xia . In the current model the left-hand- and right-hand-side variables in the constraints are inﬂuenced by hybrid uncertainty (i.e. both fuzziness and randomness); represented by fuzzy random variables (FRVs). In the ﬁrst phase, we make the best use of the chance-constrained programming approach and the α -cut approach to obtain the equivalent deterministic model of the ML-MOFP problem with FRVs. Then, the linear model of the crisp ML-MOFP problem is formulated. In the second phase, the interactive approach simpliﬁes the ML-MOLP model by changing it into isolated multi-objective decision-making (MODM) problems, to avoid non-convexity. Also, each separate MODM problem of the linear model is solved by the ε -constraint method and the concept of satisfactoriness. Finally, illustrative example and comparison with the existing techniques are provided to indicate the efﬁciency of the interactive approach.
Digital Object Identifier (DOI)
S. Osman, M.; E. Emam, O.; and A. El sayed, M.
"Interactive Approach for Multi-level Multi-objective Fractional Programming Problem under hybrid uncertainty,"
Journal of Statistics Applications & Probability: Vol. 6
, Article 11.
Available at: https://dc.naturalspublishing.com/jsap/vol6/iss3/11