Fuzzy Filtering: A Mathematical Theory and Applications in Life Science
Mohit Kumar, Kerstin Thurow, Norbert Stoll, Regina Stoll · InTech eBooks · 2010
A life science process is typically characterized by a large number of variables whose interrelations are uncertain and not completely known. The development of a computational paradigm, implementing an “intelligent” behavior in the sense of handling uncertainties related to the modeling of the interrelations among process variables, is an interesting research topic. A large number of studies apply computational intelligence techniques in the life science e.g. • in modeling the environmental behavior of chemicals (Eldred & Jurs, 1999; Kaiser & Niculescu, 1999; Gini et al., 1999; L. Sztandera et al., 2003; Sztandera et al., 2003; Vracko, 1997; Benfenati & Gini, 1997; Gini, 2000; Mazzatorta et al., 2003), • in medicine (Wilson & Russell, 2003b; Fukuda et al., 2001; Wilson & Russell, 2003a; Mandryk & Atkins, 2007; Lin et al., 2006; Rani et al., 2002; Adlassnig, 1986; Adlassnig et al., 1985; Bellazzi et al., 2001; 1998; Belmonte et al., 1994; Binaghi et al., 1993; Brai et al., 1994; Daniels et al., 1997; Fathitorbaghan & Meyer, 1994; Garibaldi & Ifeachor, 1999; Kuncheva & Steimann, 1999; Roy & Biswas, 1992; Steimann, 1996;Watanabe et al., 1994; Wong et al., 1990), • in chemistry and drug design, see e.g. (Manallack & Livingstone, 1999; Winkler, 2004; Duch et al., 2007) and references therein. The fuzzy systems based on fuzzy set theory (Zadeh, 1973; 1983) are considered suitable tools for dealing with the uncertainties. The use of fuzzy systems in data driven modeling is a topic that is widely studied by the researchers (Wang & Mendel, 1992; Nozaki et al., 1997; Shan & Fu, 1995; Nauck & Kruse, 1998; Jang, 1993; Thrift, 1991; Liska & Melsheimer, 1994; Herrera et al., 1994; Gonzalez & Perez, 1998; Babuska & Verbruggen, 1997; Babuska, 1998; Abonyi et al., 2002; Simon, 2000; 2002; Jang et al., 1997; Wang & Vrbanek, 2008; Lughofer, 2008; Kumar, Stoll & Stoll, 2009b; Lin et al., 2008; Kumar, Stoll & Stoll, 2009a) due to the successful applications of fuzzy techniques in data mining, prediction, control, classification, simulation, and pattern recognition. It is assumed that input variables (x1, x2, ... , xn) are related to the output variable y through a mapping: