Interval-Related Talks at the
Second International Conference on Fuzzy Sets
and Soft Computing in Economics and Finance
St. Petersburg, Russia, June 28—July 1, 2006
On June 28—July 1, 2006, an International Conference on Fuzzy Sets and Soft
Computing in Economics and Finance was held in St. Petersburg, Russia.
The main motivation for this conference was that in ﬁnancial and economic
situations, most parameters are known with uncertainty. It is therefore important to
take this uncertainty into account when processing ﬁnancial and economic data.
Traditionally, the uncertainty in economics and ﬁnance is described by statistical
models. This description is the basis of the current ﬁnancial mathematics, that
started largely with the Nobel-prize winning work of Black and Scholes who
applied stochastic differential equations to the pricing of options.
One of the main limitations of the traditional probabilistic approach to uncer-
tainty is that this approach requires that we known the exact values of all the relevant
In many situations in science and engineering, the processes are reasonably sta-
tionary, so in principle, by making sufﬁciently many calibration measurements, we
can determine—with reasonable accuracy—all the probabilities related to measure-
ment uncertainty. In economics and ﬁnance, however, the situation often changes; so
by the time we need to make important decisions, we do not have enough statistics
about the current situation to accurately determine all the needed probabilities.
There are two natural approaches to overcoming the above limitations.
The ﬁrst (fuzzy) approach takes into account that expert knowledge is not limited
to statistics; experts also use rules and techniques based on their previous expertise.
Experts can rarely formulate their rules in precise mathematical terms; most of these
rules are formulated by using words from natural language, like “if the price of the
stock drastically decreases, sell it.” To formulate this knowledge inside a computer,
it is reasonable to use a special technique speciﬁcally designed for formalizing such
a knowledge—the technique of fuzzy sets.
The second (interval) approach uses the fact that often, we do not know the
exact values of the probabilities and other related quantities, we only the intervals
of possible values of these quantities.
Reliable Computing (2007)