Modified fuzzy c-means for ordinal valued attributes with particle swarm for optimization
Fuzzy Sets and Systems
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Pattern vectors to be clustered may have attributes of various types including ordinal. The latter type of attribute with values such as “poor,” “very poor,” “good,” and “very good” is neither entirely numerical nor entirely qualitative. This leads to difficulties in clustering because it is meaningless to take differences of values of these ordinal attributes as is required for finding distance between pattern vectors. Representing ordinal values by numbers and then finding differences is incorrect. Rather, the ordinal values themselves may be considered as linguistic values of linguistic variables corresponding to fuzzy sets. This article discusses a method of fuzzy c-means clustering that uses fuzzy sets to represent ordinal values. Both the ratio-scaled and ordinal-scaled values can be treated in the same way by treating the ratio-scaled values as singletons. The same results are then obtained for the ratio-scaled attributes as in the traditional method. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 599–620, 2007.