Modelling Uncertainty
Jouni Smed, Harri Hakonen · 2017
This chapter focuses on both probabilistic and possibilistic uncertainty. Statistical reasoning models beliefs based on the probability of events, whereas fuzzy sets help us model the possibility of events by allowing partial membership in a set. Fuzziness can be embedded in 'classical' solution methods, and, as an example, we present how constraint satisfaction problems can be fuzzified. The chapter presents some techniques for modelling probabilistic or statistical knowledge: Bayes' theorem, Bayesian networks, and Dempster-Shafer theory. Fuzzy sets acknowledge uncertainty by allowing elements to have a partial membership in a set. In contrast to classical sets with Boolean memberships, fuzzy sets admit that some information is better than no information. Fuzzy optimization originates from ideas proposed by Bellman and Zadeh (1970), who introduced the concepts of fuzzy constraints, fuzzy objective and fuzzy decision. Each criterion associated with the problem can be fuzzified by defining a membership function which corresponds to the intuitive 'rule' behind the criterion.