# Factor Analysis with Qualitative Factors and Yager’s Probability in the Lattice of Verbal Fuzzy Numbers

Document type: Bookchapters Elisabeth Rakus-Andersson Factor Analysis with Qualitative Factors and Yager’s Probability in the Lattice of Verbal Fuzzy Numbers Issues in Soft Computing Theory and Applications 2005 2 241-260 Grzegorzewski P., Krawczak M., Zadrozny S. 83-87674-98-2 EXIT - the Publishing House of Polish Academy of Sciences Warsaw Blekinge Institute of Technology School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)School of Engineering S- 371 79 Karlskrona+46 455 38 50 00http://www.tek.bth.se/ Elisabeth.Andersson@bth.se English The classical crisp version of Factor Analysis seldom is used in the case of qualitative factors, which often are presented by codes. It is rather difficult to divide codes in level groups without possessing appropriate criteria. To omit this obstacle, we thus propose a fuzzy application of Factor Analysis, which gives a possibility to investigate the strength of an influence of qualitative factors on a tested qualitative variable. When making a new approach to the analysis of factors, we introduce a space of verbal fuzzy numbers that first are expressed as descriptions coming from a natural language and then designed in L-R form. Since the definition of newly created verbal fuzzy numbers deviates from the general conception of fuzzy numbers, we also will check effects of other operations performed on verbal numbers, which are different from the arithmetic based on the extension principle. The verbal fuzzy numbers represent both the qualitative variable and the qualitative factors in all computations that follow the Factor Analysis algorithm. For the first time we also formulate the Yager probability of an event expanded as the verbal fuzzy number. Mathematics\GeneralMathematics\Probability and Statistics verbal fuzzy numbers, max-min operations on fuzzy numbers, Yager’s probability of verbal fuzzy numbers, fuzzy factor analysis with verbal fuzzy numbers