We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept label (...) can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept label (...) can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

Modelling with Words is an emerging modelling methodology closely related to the paradigm of Computing with Words introduced by Lotfi Zadeh. This book is an authoritative collection of key contributions to the new concept of Modelling with Words. A wide range of issues in systems modelling and analysis is presented, extending from conceptual graphs and fuzzy quantifiers to humanist computing and self-organizing maps. Among the core issues investigated are - balancing predictive accuracy and high level transparency in learning - scaling (...) linguistic algorithms to high-dimensional data problems - integrating linguistic expert knowledge with knowledge derived from data - identifying sound and useful inference rules - integrating fuzzy and probabilistic uncertainty in data modelling. (shrink)

Vagueness is an extremely common feature of natural language, but does it actually play a positive, efficiency enhancing, role in communication? Adopting a probabilistic interpretation of vague terms, we propose that vagueness might act as a source of randomness when deciding what to assert. In this context we investigate the efficacy of multiple sender channels in which senders choose assertions stochastically according to vague definitions of the relevant words, and a receiver then aggregates the different signals. These vague channels are (...) then compared with Boolean channels in which assertions are selected deterministically based on classical definitions. We show that given a sufficient number of senders, a linear stochastic channel outperforms Boolean channels when performance is measured by the expected squared error between the actual value described by the senders and the receiver’s estimate of it based on the signals they receive. The number of senders required for vague channels to be at least as accurate as Boolean channels is shown to be a decreasing function of the size of the language i.e. the number of description labels available to the senders. Vague channels are then shown to be robust to transmission error provided the error rate is not too large. In addition, we investigate the behaviour of both Boolean and vague channels for a parametrised family of distributions on the input values. Finally, we consider optimal vague channels assuming a fixed number of senders and show that, provided there are more than two senders, a vague channel can be found that outperforms the optimal Boolean channel. In this context, we show that for channels with relatively low numbers of senders S-curve production functions are optimal. (shrink)