Fuzzy Mathematics in Medicine

The purpose of this book is to present a wide variety of types of fuzzy mathematics used in medical research and in the modelling of diagnostic systems. Some techniques from fuzzy mathematics include fuzzy relation equations, group decision making, abstract algebra, clustering methods, belief functions, fuzzy measures, evidence theory, Sugero integrals, abduction, automata theory, genetic algebras, and hypergraphs. Applications to medicine include medical diagnosis, bone mineral density, stroke pathogenesis, clinical monitoring, and neuronal cell-assemblies. The five basic algorithms for data analysis (clustering based on fuzzy equivalence relations, fuzzy c-means algorithm, solving a system of fuzzy relational equations, calculating fuzzy measures, and calculating the combined basic probabilistic measure) are explained in the appendix. Some of these algorithms are translated into the programming language C++.