Using fuzzy goal programming in solving quadratic bi-level fractional multi-objective programming problems.

*(English)*Zbl 1311.90135Summary: This paper presents a fuzzy goal programming (FGP) technique for solving quadratic bi-level fractional multi-objective programming (QBL-FMOP) problems. The present approach is an extension work of B. B. Pal and B. N. Moitra [Int. J. Intell. Syst. 18, No. 5, 529–540 (2003; Zbl 1038.68027)] and I. A. Baky [Fuzzy Sets Syst. 160, No. 18, 2701–2713 (2009; Zbl 1181.90300)]. In a bi-level programming problem (BLPP), two decision makers (DMs) are located at two different hierarchical levels, each independently controlling one set of decision variables with different and perhaps conflicting objectives. In the present article both the lower level decision maker (LLDM) and upper level decision maker (ULDM) solve the problem for the decision variables and if the obtained result is not satisfactory from the DMs point of view, then both the DMs make a balance of decision powers i.e. the leader and follower would have to give possible relaxations of their decisions which depends on the decision-making context. At the first phase of the solution process, we transform the fractional quadratic programming model into an equivalent nonlinear quadratic problem. In this stage the above obtained quadratic problem is again transformed into an equivalent linear membership function by using first order Taylor series expansion. An illustrative numerical example is given in the end to demonstrate the procedure.

##### MSC:

90C29 | Multi-objective and goal programming |

90C20 | Quadratic programming |

90C32 | Fractional programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |