A fuzzy graph is a representation tool for many real networks. But, due to some restriction on edges, fuzzy graphs are limited to represent for some networks. In this study, generalized fuzzy graphs and generalized directed fuzzy graphs are discussed to avoid such restrictions. A pipeline network is expressed as a generalized directed fuzzy graph. In the pipeline network, the generalized membership values of edges and vertices are determined by the capacity of the pipelines. Also, fuzzy r-cuts and fuzzy (r 1, r 2,..., r n)-cuts in the generalized fuzzy graphs are defined.
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In this study, two types of generalized fuzzy graphs namely GFG1, GFG2 were discussed. Also, the generalized directed fuzzy graphs, GDFG1, GDFG2 were defined. These graphs can be assumed as the generalisation of graphs as well as fuzzy graphs. A method to compute membership functions was discussed. Then, fuzzy r-cuts were introduced and extended to fuzzy n tuple cut. Any networks and images can be represented by the generalized fuzzy graphs. Image segmentation has many modern techniques. One of the graph based methods is graph cuts. Ford-Fulkerson algorithm is one of the important algorithms regarding graph cuts. But, Ford-Fulkerson algorithm cannot be applied to generalized fuzzy graphs as the main assumption of the algorithm is that all capacities are integers. Different energy functions This work was supported by the research fund of Hanyang University (HY-2018-F), (Project Number 201800000001370).
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Artificial Intelligence