In this paper, we present a novel fully distributed topology control protocol that can construct the multiple-ring topology of Minimal Connected Dominating Set (MCDS) as the transport backbone for mobile ad hoc networks. It makes a topology from the minimal nodes that are chosen from all the nodes, and the constructed topology is comprised of the minimal physical links while preserving connectivity. This topology reduces the interference. The all nodes work as the nodes of the distributed parallel Boltzmann machine, of which the objective function is consisted of two Boltzmann factors: the link degree and the connection domination degree. To define these Boltzmann factors, we extend the Connected Dominating Set into a fuzzy set, and also define the fuzzy set of nodes by which the multiple-ring topology can be constructed. To construct the transport backbone of the mobile ad hoc network, the proposed protocol chooses the nodes that are the strong members of these two fuzzy sets as the clusterheads. We also ran simulations to provide the quantitative comparison against the related works in terms of the packet loss rate and the energy consumption rate. As a result, we show that the network that is constructed by the proposed protocol has far better than the other ones with respect to the packet loss rate and the energy consumption rate.