Assessing interestingness of fuzzy rules using an ordinal framework

There are many studies in the data mining of fuzzy rules of the form Educated boolean AND HighIncome double right arrow GoodCredit where Educated, HighIncome and GoodCredit are linguistic terms defined as fuzzy sets in a common domain. We have pointed out in an earlier paper [3] that in assessing interestingness of such rule using commonly defined rule confidence, normally two assumptions are made. Firstly, the fuzzy set membership functions are assumed to have quantitative semantics so that membership values can be quantitatively manipulated. Secondly, the scales used in the different membership functions are assumed to be commensurate with one another so that they can be compared and combined. Different choices of membership functions may lead to significantly different assessment of rule confidence. We proposed a new interpretation of fuzzy rules of the form X boolean AND Y double right arrow Z and a measure of the nile significance that will avoid the above implicit assumptions and hence more robust. The measure treats fuzzy membership functions as ordinal scales and makes no assumption of the scales being the same thus making this measure more robust. In this paper we discuss a dynamic programming approach for the evaluation of this measure.