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A Method for Fuzzy Clustering with Ordinal Attributes Replaced by Fuzzy Set Parameters

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" are neither entirely numerical nor entirely qualitative. This leads to difficulties in clustering since 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 are incorrect. Rather the ordinal values themselves may considered as linguistic values of linguistic variables corresponding to fuzzy sets. This paper discusses a method of fuzzy c-means clustering that uses the moments and areas of fuzzy sets to represent the value of ordinal attributes and also the continuous values of the interval scaled attributes