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**Interactive fuzzy goal programming approach for bilevel programming problem.**
*(English)*
Zbl 1154.90583

Summary: This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP).

In the proposed approach, the tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the objectives of both the decision makers and degree of achievement of the decision vector controlled by the leader is defined first. Then the dynamic fuzzy goal programming model for achievement of highest degree (unity) to the extent possible to each of the defined membership functions for the fuzzy goal is developed to solve the decisions of the interrelated stages. A satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers with the consideration of overall satisfactory balance between both the levels. Illustrative numerical examples are provided to demonstrate the feasibility of the proposed method.

In the proposed approach, the tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the objectives of both the decision makers and degree of achievement of the decision vector controlled by the leader is defined first. Then the dynamic fuzzy goal programming model for achievement of highest degree (unity) to the extent possible to each of the defined membership functions for the fuzzy goal is developed to solve the decisions of the interrelated stages. A satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers with the consideration of overall satisfactory balance between both the levels. Illustrative numerical examples are provided to demonstrate the feasibility of the proposed method.

### MSC:

90C29 | Multi-objective and goal programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C39 | Dynamic programming |

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\textit{S. R. Arora} and \textit{R. Gupta}, Eur. J. Oper. Res. 194, No. 2, 368--376 (2009; Zbl 1154.90583)

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