An exchange economy is considered, where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities. Pricing formulas and risk allocations, generalising the results of Bühlmann (1980, 1984) are obtained via the construction of aggregate pre...

‎ranking fuzzy numbers is generalization of the concepts of order, and class, and so have fundamental applications. moreover, deriving the final efficiency and powerful ranking are helpful to decision makers when solving fuzzy problems. selecting a good ranking method can apply to choosing a desired criterion in a fuzzy environment. there are numerous methods proposed for the ranking of fuzzy n...

Consider an urn holding 101 balls, each marked with a number from 1 through 4. You don’t know the number of balls of each type, but you do know that exactly 50 are marked with either a 1 or a 2, and 51 are marked with either a 3 or a 4. This is a variation on the classic urns of Daniel Ellsberg (1961). Given its information structure, you don’t know the probability of any given number being dra...

We give a new and simple proof of a key lemma on the rank of a matrix in Leung's paper [3], where he showed there exists a family of nondeterministic nite automata fAng, with n states and exponential ambiguity, such that any smallest equivalent polynomially ambiguous nite automaton has 2 1 states. Keyword: nondeterministic automata, ambiguity, automata theory.

List-wise learning to rank methods are considered to be the stateof-the-art. One of the major problems with these methods is that the ambiguous nature of relevance labels in learning to rank data is ignored. Ambiguity of relevance labels refers to the phenomenon that multiple documents may be assigned the same relevance label for a given query, so that no preference order should be learned for ...

In GPS data processing it is not uncommon to eliminate the presence of ionospheric delays by taking certain linear combinations of the carrier phase data. This approach is in fact equivalent with a processing of the original, not combined, L1 and L2 phase observations in which the ionospheric delays are modelled as unknown parameters. When using phase data only, the presence of the unknown iono...