Atanassov's intuitionistic fuzzy probability and Markov chains

Fuzzy probabilities are an extension of the concept of probabilities with application in several practical problems. The former are probabilities represented through fuzzy numbers, to indicate the uncertainty in the value assigned to a probability. Moreover, Krassimir Atanassov in 1983 added an extra degree of uncertainty to classic fuzzy sets for modeling the hesitation and uncertainty about the degree of membership. This new theory of fuzzy sets is nowadays known as Atanassov intuitionistic fuzzy set theory. This work will extend the notion of fuzzy probabilities by representing probabilities through the Atanassov intuitionistic fuzzy numbers instead of fuzzy numbers. (C) 2013 Elsevier B.V. All rights reserved.