Fuzzy and Rough Techniques in Medical Diagnosis and Medication

In the late eighties of the twentieth century I encountered a paper referring to mathematics dealing with imprecision applied to medical diagnosis. I was working in the area of medical statistics at that time, and obviously I was interested in the contents of the paper. After I had read it I became fascinated by new possibilities of medical data interpretation and processing proposed by the author. The new world of fuzziness, originated by Professor Lotfi Zadeh, seemed to open up to me and I started reading all accessible material about fuzzy set theory. Many years have passed since then. We are now living in the information so- ety and we do not experience troubles in reaching scientific material. Lately I have read many papers and books about treating medical tasks solved by using fuzzy ideas. I am still keen on tracing applications in medicine, and by myself I have been contributing to some concepts in this subject that has motivated me to p- pare my own book. The objective of writing such a book has been a little parti- lar, namely, I have intended to present the subject of fuzzy tools and techniques in medicine for eventual users. These, maybe representatives of medical or phar- cological staffs, are not expected to possess a large amount of mathematical knowledge.

This volume provides readers with selected fuzzy and rough tools used to medical tasks, especially diagnosing and medication. To build a link between theoretical, mathematical excerpts and practical medical applications, the contents is formed as a sequence of occurrences in which a patient appears to be diagnosed and cured. The fuzzy and rough elements are inserted in the book in the order required by the presentation of medical substance to maintain the logical unity of the book’s essence.

In conformity with this pattern the essay presents in turn some necessary elements of fuzzy set theory, the classical fuzzy diagnostic model with extensions, the fuzzy diagnostic model with clinical examinations extended throughout time based on distance theory, methods of drug effectiveness measurements and algorithms selecting the optimal medicine. As the complement, the solution of an approximation problem is suggested to find a curve that surrounds two-dimensional clock-like point sets with the little approximation error.

A lot of appealing examples are added to facilitate comprehension of theoretical principles for a reader, so that even a beginner in fuzzy set theory can follow calculation steps without implementing computer programs. It should be emphasized that all models are also applicable to other fields, especially to technical domains after necessary adaptations. This confirms the existence of the large spectrum of applicable fuzzy and rough methods not only in medicine but also in natural sciences.