# Fuzzy and Rough Set Theory in Treatment of Elderly Gastric Cancer Patients

Document type: Licentiates Lic Hang Zettervall.pdf Hang Zettervall Fuzzy and Rough Set Theory in Treatment of Elderly Gastric Cancer Patients Blekinge Institute of Technology Licentiate Dissertion Series 2011 3 978-91-7295-202-7 1650-2140 Blekinge Institute of Technology Karlskrona Blekinge Institute of Technology School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)School of Engineering S-371 79 Karlskrona+46 455 38 50 00http://www.bth.se/ing/ hang.zettervall@bth.se English Fuzzy set theory was presented for the first time by Professor Lotfi A. Zadeh from Berkeley University in 1965. In conventional binary logic a statement can be true or false, and there is no place for even a little uncertainty in this judgment. An element either belongs to a set or does not. We call these kinds of sets crisp sets. In practice we often experience those real situations that are represented by crisp sets as impossible to describe accurately. A two-valued logic assumes that precise symbols must be employed, and it is therefore not applicable to the real existence. If the information demanded by a system is lacking, the future state of such a system may not be known completely. One of the instruments used to handle the vagueness in the real-world situations is fuzzy set theory, which has been frequently applied in a wide range of areas like, e.g., dynamic systems, militaries, medicine and other domains. Another theory, which copes with the problem of imprecision, is known as rough set theory. It was proposed by Professor Zdzisław Pawlak in Warsaw in the 1980ties. Whereas imprecision is expressed in the category of a membership degree in fuzzy set theory, this is a matter of the set approximation in rough set theory. Due to the definition of a rough set formulated by means of the decision attribute value, two approximate sets of the rough set are determined. These contain sure and possible members of the universe considered, in which the rough set has been defined.One of the objectives of this study is to apply some classical methods of fuzzy set theory to medicine in order to estimate the survival length of gastric cancer patients. We have decided to test the action of fuzzy controllers of the Mamdani and Sugeno type. Two clinical markers, playing roles of the independent variables, have been included in the algorithm as the base information assisting the survival prognosis. Since the model results have been convergent to the expected experimental values then we will intend to make some extensions of the model concerning the larger number of independent variables. We have also utilized rough set classification, to verify the types of operations. These items are discussed in the thesis in conformity with the physicians’ wishes to support results of statistical investigations. The current research is funded by the scientific grant obtained from Blekinge Research Board. Mathematics\General Lic. March 25th urn:nbn:se:bth-00489