Conventional models of navigation commonly assume a navigation agent’s location can be precisely determined. This paper examines the more general case, where an agent’s actual location cannot be precisely determined. This paper develops a formal model of navigation under imprecision using a graph. Two key strategies for dealing with imprecision are identified and defined: contingency and refine...

We present a concise overview of imprecise reliability, particularly focussing on reliability theory with uncertainty quantified via lower and upper probabilities. We discuss the main approaches and opportunities of the theory, we include references to guide further study, and we briefly discuss some research challenges.

in the portfolio selection problem, the manager considers several objectives simultaneously such as the rate of return, the liquidity and the risk of portfolios. these objectives are conflicting and incommensurable. moreover, the objectives can be imprecise. generally, the portfolio manager seeks the best combination of the stocks that meets his investment objectives. the imprecise goal program...

envelopment analysis (dea) is a very eective method to evaluate the relative eciency of decision-making units (dmus). dea models divided all dmus in two categories: ecient and inecientdmus, and don't able to discriminant between ecient dmus. on the other hand, the observedvalues of the input and output data in real-life problems are sometimes imprecise or vague, suchas interval data, ...

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley’s behavioural theory of imprecise probabilities, and Shafer and Vovk’s game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that...

Since almost all objects of mathematics can be described by sets (e.g., a function as a set of ordered pairs), one can establish fuzzy generalizations for nearly all of those. In the previous sections, we have seen that fuzzy mathematical concepts occur ‘naturally’, that is, considering the uncertainty involved in the application, the need to generalize creates fuzzy mathematical objects. We co...

1 Overview Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P (A) is used, typically satisfying Kolmogorov's axioms [4]. Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and co...

Imprecise inference models the ability to infer sets of values or information chunks. Imprecise database inference is just as important as precise inference. In fact, it is more prevalent than its precise counterpart even in precise databases. Analyzing the extent of imprecise inference is important in knowledge discovery and database security. Imprecise inference analysis can be used to \mine"...

Several methods have been proposed for ranking the decision-making units (DMUs) in data envelopment analysis (DEA) with imprecise data. Some methods have only used the upper bound efficiencies to rank DMUs. However, some other methods have considered both of the lower and upper bound efficiencies to rank DMUs. The current paper shows that these methods did not consider the DEA axioms and may be...