# An Application of Fuzzy Numbers in Eigen Fuzzy Set Problem to Differentiating the Effectiveness of Drugs

Document type: Conference Papers Yes Elisabeth Rakus-Andersson An Application of Fuzzy Numbers in Eigen Fuzzy Set Problem to Differentiating the Effectiveness of Drugs En tillämpning på oskarpa nummer i en oskarp egenvektor som en metod att urskilja en effekt av medicininverkan Fuzzy Information Processing. Theories and applications 2003 85-90 7-302-06299-4 Tsinghua University Press - Springer Beijing, China Blekinge Institute of Technology Department of Health, Science and Mathematics (Institutionen för hälso- och naturvetenskap)Dept. of Health, Science and Mathematics S-371 79 Karlskrona+46 455 38 50 00http://www.bth.se/ihn/ Elisabeth.Andersson@bth.se English The fuzzy technique revealed in this paper is a new attempt of solving the problem of appreciating the effectiveness level of a medicine when using it against the symptoms typical of a morbid unit. To obtain a satisfactory result, a fuzzy relation with elements equal to fuzzy numbers in L-R representation is introduced. The fuzzy numbers that appear in the relation replace the verbal expressions decided by physicians in accordance with the definition of the relation. The fuzzy relation filled with the fuzzy numbers, which is a counterpart of the average fuzzy relation with the real numbers, also has its eigen fuzzy set with membership degrees as fuzzy numbers. These, after taking appropriate places in the eigen fuzzy set, appreciate the levels of the drug influence on the clinical symptoms. Artikeln presenterar användning av oskarp egenvektor i processen approximeringen av läkemedelsverkan på kliniska symptom. En oskarp relation, introducerad i en ”fuzzy” ekvation med lösningen lika med den oskarpa egenvektorn, innehåller oskarpa nummer som uttrycker läkemedelsinverkan på parsymtom. Dessa nummer, skapade i L-Rformen ersätter verbala beskrivningar av påverkan. Det resultat, som visar läkemedelsnivåer vid varje symtom, fås genom en tolkning av oskarpa nummer i den erhållna egenvektorn. Mathematics\General Fuzzy numbers in fuzzy relations, The eigen set of a fuzzy relation, Aggregation operations, The appreciation of drug effectiveness levels