Rubinstein, Safra and Thomson (1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social cho...

Background. Historically, most acute stroke clinical trials were neutral statistically, with trials typically dichotomising ordinal scales, such as the modified Rankin Scale. Studies published before 2007 have shown that preserving the ordinal nature of these scales increased statistical power. A systematic review of trials published since 2007 was conducted to reevaluate statistical methods us...

‎‎in this paper‎, ‎we define fuzzy subnexuses over a nexus $n$‎. ‎define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎finally‎, ‎we show that if s is a meet‎‎closed subset of the set fsub(n), ‎of fuzzy subnexuses of a nexus n‎, ‎and‎‎h= ⋀s ϵ s, ‎then the fractions s^-1 n and h^-1 n are isomorphic as meet-semilattices‎.

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel’s constructible universe L. This characterization can be used to prove the generalized continuum...

How do ordinals measure the strength and computational power of formal theories and what information can be gleaned from this correlation? This will be the guiding question of this talk. The connection between ordinal representation systems and theories is established in ordinal analysis, a central area of proof theory. Ordinal-theoretic proof theory came into existence in 1936. Gentzen showed ...

(A for ‘above’; B for ‘below.’) A lattice satisfying this condition is called finitely separable. It is easy to see that every countable lattice is finitely separable. We used this to show the following surprising result: the ordinal sum of two free lattices is projective if and only if one of them is finitely generated or both are countable. In this note we give a complete characterization of ...

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial fun...

In this paper, we present an ordinal feature based method for face recognition. Ordinal features are used to represent faces. Hamming distance of many local sub-windows is computed to evaluate differences of two ordinal faces. AdaBoost learning is finally applied to select most effective hamming distance based weak classifiers and build a powerful classifier. Experiments demonstrate good result...