interval-based uncertain reasoning
abstract
this thesis examines three interval based uncertain reasoning approaches: reasoning
under interval constraints, reasoning using necessity and possibility functions, and
reasoning with rough set theory. in all these approaches, intervals are used to characterize
the uncertainty involved in a reasoning process when the available information
is insufficient for single-valued truth evaluation functions. approaches using interval
constraints can be applied to both interval fuzzy sets and interval probabilities. the
notion of interval triangular norms, or interval t-norms for short, is introduced and
studied in both numeric and non-numeric settings. algorithms for computing interval
t-norms are proposed. basic issues on the use of t-norms for approximate reasoning
with interval fuzzy sets are studied. inference rules for reasoning under interval constraints
are investigated. in the second approach, a pair of necessity and possibility
functions is used to bound the fuzzy truth values of propositions. inference in this
case is to narrow the gap between the pair of the functions. inference rules are derived
from the properties of necessity and possibility functions. the theory of rough sets
is used to approximate truth values of propositions and to explore modal structures
in many-valued logic. it offers an uncertain reasoning method complementary to the
other two.
collections
- retrospective theses [1604]