Developing resource allocation algorithms for the uplink sparse code multiple access (SCMA) scheme to satisfy multiple objectives is challenging, especially where users are randomly distributed. In this paper, we aim to address this challenge by developing a joint resource allocation method as a multi-objective optimization (MO) problem to maximize the average sum rate and fairness among users as key and sub-key objectives, respectively. For this purpose, the exact analytical expressions for the average sum rate and users' individual rate are extracted based on an adaptive weighted graph matrix (AWGM). An AWGM matrix beneficially replaces the factor graph and the power allocation matrices to simplify the MO problem based on the asymmetric modified bipartite matching (AMBM) algorithm. The power allocation strategy is utilized during the optimal resource assignment process using the AMBM algorithm. After the AMBM process, we propose a low-complexity four-step algorithm to obtain the AWGM. The simulation results show that our proposed method can compromise and improve the multiple objectives' performance and guarantees a stable range of network performance at different times.