Covering of an Ordinal Attribute with Fuzzy Sets for Fuzzy Clustering

R.K. Brouwer (Canada)


Fuzzy clustering, ordinal values, ordinal regression, attribute vectors


This paper describes development of a method for representing an ordinal attribute by a covering of fuzzy sets rather than a set of natural numbers as is the usual practice. Attribute vectors that represent objects to be clustered may have some components that are numerical and other components that are non-numerical. The non-numerical ones may be nominal ( also called categorical) or ordinal. Ordinal values cannot be replaced by index values with equal differences between the index values since that would be making an incorrect assumption. The only thing that is known about the ordinal values is the order. However if a frequency distribution is provided for the ordinal values and an assumption of normality is made it is still possible to find fuzzy sets that represent these ordinal values that is more accurate than the simple replacing of the ordinal values with equally spaced index values. The method is shown to be quite successful.

Important Links:

Go Back