Fuzzy graphs can also be weighted (that is supported in FuzzPy), but represent a set of fuzzy elements and their connections, so you are just dealing with a different type of member elements.
Also, since your graph elements are all members of a fuzzy set, you can also perform fuzzy set operations against your vertices or edges, whereas using weights for this type of work might often yield useless results.
I have a use case for this in a wargame with hidden units. You know the size of an opponent's stacks, and the total forces he commands, but not always which units are in which stacks. But you can observe some, and deduce some, and guess some.
I'm using fuzzy subsets of Euclidean 3-space to model sensor coverage. Computationally, I use FuzzPy's (discrete) fuzzy set class to make fuzzy sets of 3D point objects to work with.
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In what sense is a "fuzzy graph" different than a standard weighted graph?
http://en.wikipedia.org/wiki/Weighted_graph#Weighted_graphs_...
Fuzzy graphs can also be weighted (that is supported in FuzzPy), but represent a set of fuzzy elements and their connections, so you are just dealing with a different type of member elements.
Also, since your graph elements are all members of a fuzzy set, you can also perform fuzzy set operations against your vertices or edges, whereas using weights for this type of work might often yield useless results.
Can anyone elaborate on some applications of fuzzy sets? I'm guessing something like strength of relationships in given social graphs as an example.
Fuzzy Sets can be used in a pretty wide variety of fields. Here are three books by the same author that cover a pretty big area:
http://www.amazon.com/Modeling-Algorithms-Exploration-Kaufma...
http://www.amazon.com/Fuzzy-Logic-Business-Industry-Windows/...
http://www.amazon.com/Fuzzy-Systems-Handbook-Second-Practiti...
I have a use case for this in a wargame with hidden units. You know the size of an opponent's stacks, and the total forces he commands, but not always which units are in which stacks. But you can observe some, and deduce some, and guess some.
I'm using fuzzy subsets of Euclidean 3-space to model sensor coverage. Computationally, I use FuzzPy's (discrete) fuzzy set class to make fuzzy sets of 3D point objects to work with.