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**A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming.**
*(English)*
Zbl 1012.90074

Summary: This paper describes how the preemptive priority based goal programming (GP) can be used to solve a class of fuzzy programming (FP) problems with the characteristics of dynamic programming (DP).

In the proposed approach, the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first. Then, under the framework of preemptive priority based GP a multi-stage DP model of the problem for achievement of the highest degree (unity) of each of the membership functions is developed. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution. Two numerical examples are provided to illustrate the approach.

In the proposed approach, the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first. Then, under the framework of preemptive priority based GP a multi-stage DP model of the problem for achievement of the highest degree (unity) of each of the membership functions is developed. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution. Two numerical examples are provided to illustrate the approach.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C29 | Multi-objective and goal programming |

90C39 | Dynamic programming |

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\textit{B. B. Pal} and \textit{B. N. Moitra}, Eur. J. Oper. Res. 144, No. 3, 480--491 (2003; Zbl 1012.90074)

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