Data Driven Generation of Fuzzy Systems: An Application to Breast Cancer Detection

The detection of diseases often can be formalized as a decision problem that typically has to be solved merging uncertain information; diagnostic tools, intended to aid the physician in interpreting the data, besides attaining the best possible correct classification rate, should furnish some insight into how the problem has been decided. Fuzzy logic is a well known successful attempt to automatize the human capability to reason with imperfect information; fuzzy systems are rule-based so that they can easily provide motivations for their decisions, after having verified some additional conditions. In this paper we describe a six-steps data driven methodology to automatically build fuzzy systems with a user defined number of rules; almost each step can be approached using several strategies and we thus describe an implementation of the proposed solution. Then, we test our systems on a well known and widely used data set of features of images of breast masses and, having the number of rules varying, we show results both in terms of correct classification rates and in terms of systems' confidence in the obtained decisions. Finally, we select the number of rules that produces the most interpretable and trustworthy system; such a system is described in details and tested.