A New Algorithm for Solving Maximal Flow Problem in an Intuitionistic Fuzzy Network

The maximal flow problem is consider as one of the classic combinatorial optimization problems and hence gradually becomes the area of interests for the researchers and engineers. But in real life there exist uncertainty in the capacity as well as in the flow parameters of an arc of a network. Finding the maximum flow between the source and destination nodes of a network with uncertainties in its flow and capacities has many applications in different domains such as electrical powers, traffics, communications, computer networks and logistics. In this paper the classical Ford-Fulkerson algorithm for maximal flow problem has been modified to find the maximum flow of an network where the flow capacity of each arc is expressed as intuitionistic normal fuzzy numbers (INFNs) having degree of acceptance and degree of rejection. The Improved Intuitionistic Fuzzy Maximal Flow Algorithm (IIFMFA) proposed in this paper can solve intuitionistic normal fuzzy maximal flow problem (INFMFP) using intuitionistic normal fuzzy order weighted geometric averaging (INFOWGA) aggregation operator. To validate the proposed algorithm a numerical example is presented where we compare the augmenting flow chains of a crisp network with that of an intuitionistic fuzzy network.