Fuzzy and crisp set-theoretic-based classification of health and disease. A qualitative and quantitative comparison

Conventional cluster analyses of patient populations are intended to assist in the identification and characterization of groups that may represent etiological or pathological subtypes within a particular disease class. These methods have been criticized as being insensitive to subtle patient differences, which may be masked as a result of the all-or-nothing concept of cluster membership intrinsic to crisp set-theoretic-based grouping algorithms. As an alternative to conventional clustering procedures, several investigators have studied the use of fuzzy classification methods. In general, these measure a patient's clinical status in terms of a real number defined on the closed unit interval, reflecting the extent or degree to which a particular grouping entity characterizes the patient. This paper compares and contrasts the applications of crisp and fuzzy set-theoretic-based clustering procedures to a set of data describing the cognitive and intellectual functioning of a group of subjects participating in a longitudinal study of aging. Emphasis is placed on both qualitative and quantitative aspects corresponding, respectively, to the clinical interpretation of cluster definitions, and the robustness or sensitivity of the classification procedures to changes in patient profiles over time. The fuzzy set-theoretic-based model was found to be more sensitive to changes in subject level of functioning over time, to provide superior quantitative protrayals of patterns of aging, and to reflect properties of the aging process derived from other research.