Unified approach to fuzzy graph problems

We present a taxonomy of fuzzy graphs that treats fuzziness in vertex existence, edge existence, edge connectivity, and edge weight. Within that framework, we formulate some standard graph-theoretic problems (shortest paths and minimum cut) for fuzzy graphs using a unified approach distinguished by its uniform application of guiding principles such as the construction of membership grades via the ranking of fuzzy numbers, the preservation of membership grade normalization, and the "collapsing" of fuzzy sets of graphs into fuzzy graphs. Finally, we provide algorithmic solutions to these problems, with examples.

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