  It is common to encounter the situation with uncertainty for decision makers
(DMs) in dealing with a complex decision making problem. The existing evidence
shows that people usually fear the extreme uncertainty named as the unknown.
This paper reports the modified version of the typical regret theory by
considering the fear experienced by DMs for the unknown. Based on the responses
of undergraduate students to the hypothetical choice problems with an unknown
outcome, some experimental evidences are observed and analyzed. The framework
of the modified regret theory is established by considering the effects of an
unknown outcome. A fear function is equipped and some implications are proved.
The behavioral foundation of the modified regret theory is further developed by
modifying the axiomatic properties of the existing one as those based on the
utility function; and it is recalled as the utility-based behavioral foundation
for convenience. The application to the medical decision making with an unknown
risk is studied and the effects of the fear function are investigated. The
observations reveal that the existence of an unknown outcome could enhance,
impede or reverse the preference relation of people in a choice problem, which
can be predicted by the developed regret theory.
