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approach the personal preference of the decision maker by modeling the deliberating
process during decision making. It is mainly a trade-off between several conflict or
incoherent subjective attributes in the subjective deliberating space. The model
adopted here should be capable of accounting for the different 'irrational' phenome-
non in human decision making behavior studies, so that the personalized choice set
will be more human like. Here we choose Multi-alternative Decision Field Theory
(MDFT) [11] that meets all these needs.
2.3 MDFT
MDFT is the expansion of DFT which was proposed by Jerome Busemeyer and Jim
Townsend [9] in 1993. MDFT provides a mathematical foundation that leads to a
dynamic, stochastic theory of decision behavior in an uncertain environment. Accord-
ing to MDFT, decisions are based on preference states, P(t), representing the momen-
tary preference for choosing one alternative over the other in a binary choice or others
in the ternary choices—for instance, A over B or A over B and A over C. That is, P(t)
reflects the relative strength of preference of choosing A over B or A over B and C at
time t. Preference evolves over time and is updated by an input valence, reflecting the
momentary comparison of consequences produced by thinking of the different choic-
es. The valence fluctuates because the decision maker's attention switches back and
forth between anticipated consequences. The decision maker draws information about
the alternatives from his or her memory. The possible consequences connected with
either alternative are learned from experience and are remembered more or less well.
A decision is made as soon as the preference process reaches a decision criterion or
threshold for any one of the alternatives. The dynamics of the preference process is
formally described according to the following stochastic process:
PthSPtVth
(1)
Where,
P(t) is the preferences matrix of the alternative choices at time t;
S is the inhibition matrix. It is decided by the psychological distance of the two
compared alternatives.
While
VtCtMtWt
(2)
C(t) is the contrast matrix, represents the process used to compare options;
For three alternatives,
1 0.5 0.5
0.5 1 0.5
0.5 0.5 1
Ct
(3)
M(t) stands for the attributes' matrix in subjective deliberating space;
