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In this paper, a device-to-device (D2D) communications multiple-metric scenario for resource allocation and pairing is studied. To improve the D2D connection stability, a fuzzy method based on the data rate and battery levels of potential D2D pairs is proposed in such a way that the set of D2D transmitters is considered as a fuzzy set. A single cell scenario with a cellular user and some co-channel D2D nodes consists of D2D receivers, and transmitters are taken into account. Furthermore, a stable fuzzy pairing criterion is proposed for the selection of the best D2D transmitter. The proposed method is compared with three other pairing methods named the maximum sum rate, constant pairing method, and random pairing method. The simulation results show that the mentioned pairing method outperforms the other three methods in terms of stability and fairness criteria and follows the maximum sum-rate method from the sum-rate criteria point of view.