The allocation of multiple types of resources fairly and efficiently has become a substantial concern in state-ofthe-art computing systems. Accordingly, the rapid growth of cloud computing has highlighted the importance of resource management as a complicated and NP-hard problem. Unlike traditional frameworks, in modern data centers, incoming jobs pose demand profiles, including diverse sets of resources such as CPU, memory, and bandwidth across multiple servers. Accordingly, the fair distribution of resources, respecting such heterogeneity appears to be a challenging issue. Furthermore, the efficient use of resources as well as fairness, establish trade-off that renders a higher degree of satisfaction for both users and providers. Dominant Resource Fairness (DRF) has been introduced as an initial attempt to address fair resource allocation in multi-resource cloud computing infrastructures. Dozens of approaches have been proposed to overcome existing shortcomings associated with DRF. Although all those developments have satisfied several desirable fairness features, there are still substantial gaps. Firstly, it is not clear how to measure the fair allocation of resources among users. Secondly, no particular trade-off considers non-dominant resources in allocation decisions. Thirdly, those allocations are not intuitively fair as some users are not able to maximize their allocations. In particular, the recent approaches have not considered the aggregate resource demands concerning dominant and non-dominant resources across multiple servers. These issues lead to an uneven allocation of resources over numerous servers which is an obstacle against utility maximization for some users with dominant resources. Correspondingly, in this paper, a resource allocation algorithm called H-FFMRA is proposed to distribute resources with fairness across servers and users, considering dominant and non-dominant resources. The experiments show that H-FFMRA achieves approximately %20 improvements on fairness as well as full utilization of resources compared to DRF in multi-server settings.