93,226 research outputs found
Interval-based uncertain reasoning
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
Modelling potential movement in constrained travel environments using rough space-time prisms
The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space-time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space-time points in obstacle-constrained travel environments
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
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