  The sure thing principle and the law of total probability are basic laws in
classic probability theory. A disjunction fallacy leads to the violation of
these two classical laws. In this paper, an Evidential Markov (EM) decision
making model based on Dempster-Shafer (D-S) evidence theory and Markov
modelling is proposed to address this issue and model the real human
decision-making process. In an evidential framework, the states are extended by
introducing an uncertain state which represents the hesitance of a decision
maker. The classical Markov model can not produce the disjunction effect, which
assumes that a decision has to be certain at one time. However, the state is
allowed to be uncertain in the EM model before the final decision is made. An
extra uncertainty degree parameter is defined by a belief entropy, named Deng
entropy, to assignment the basic probability assignment of the uncertain state,
which is the key to predict the disjunction effect. A classical categorization
decision-making experiment is used to illustrate the effectiveness and validity
of EM model. The disjunction effect can be well predicted and the free
parameters are less compared with the existing models.
