@InBook{Navara:tmeas_ch, IS = { zkontrolovano 19 Dec 2005 }, UPDATE = { 2005-12-14 }, author = {Mirko Navara}, title = {Triangular norms and measures of fuzzy sets}, year = {2005}, pages = {345--390}, chapter = {13}, editor = {Erich Peter Klement and Radko Mesiar}, publisher = {Elsevier}, address = {Amsterdam, The Netherlands}, isbn = {0-444-51814-2}, book_pages = {492}, volume = {Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms}, edition = {1}, importance = {1}, authorship = {100}, annote = {The classical measure and probability theory is based on the notion of Sigma-algebra of subsets of a set. Butnariu and Klement generalized it to fuzzy sets by considering collections of fuzzy sets called T-tribes (where T denotes a fixed triangular norm). Their concept of T-measure is fundamental in the fuzzification of classical measure theory. However, it has been successfully applied elsewhere, too (e.g., in finding solutions to games with fuzzy coalitions). Here we summarize results about characterization of measures on tribes. More generally, we study signed measures (called charges). Unlike preceding papers, we put emphasis on s-order continuous charges which preserve limits of increasing as well as decreasing sequences of fuzzy sets. We argue that this notion could be considered as a promising alternative to the original notion of Butnariu and Klement.}, keywords = {fuzzy set, triangular norm, tribe, measure, probability, state, order continuity}, type = {chapter}, project = {GACR 201/02/1540, CEEPUS SK-042}, psurl = {[PDF]}, www = {http://www.elsevier.com/wps/find/bookdescription.cws_home/705173/description#description }, }