While smooth exact potential games are easily characterized in terms of the crossderivatives of players’payo¤ functions, an analogous di¤erentiable characterization of ordinal or generalized ordinal potential games has been elusive for a long time. In this paper, it is shown that the existence of a generalized ordinal potential in a smooth game with multidimensional strategy spaces is crucially...

We present ordinal measures of association for image correspondence in the context of stereo. Linear correspondence measures like correlation and the sum of squared diier-ence between intensity distributions are known to be fragile. Ordinal measures which are based on relative ordering of intensity values in windows { rank permutations { have demonstrable robustness. By using distance metrics b...

We introduce a notion of join for (augmented) simplicial sets gen-eralising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category ∆.

We present ordinal measures of association for establishing visual correspondence in images. Linear correspondence measures like correlation and the sum of squared differences are known to be fragile. Ordinal measures, which are based on relative ordering of intensity values in windows, have demonstrable robustness to depth discontinuities, occlusion, and noise. The relative ordering of intensi...

We present ordinal measures of association for image correspondence in the context of stereo. Linear correspondence measures like correlation and the sum of squared difference between intensity distributions are known to be fragile. Ordinal measures which are based on relative ordering of intensity values in windows—rank permutations—have demonstrable robustness. By using distance metrics betwe...

Quasivarieties of distributive double p-algebras generated by an ordinal sum M of two Boolean lattices are considered. Globally minimal failsets within S(M2) are completely determined; from them all the optimal dualities for these quasivarieties are obtained.

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an binary operations (not necessarily t-norms) defined the fixed subintervals may not be t-norm. Some necessary and sufficient conditions are presented in this article for ensuring that two is, fact, In particular, results here provide answer open problem put forward by Ertuğrul Yeşilyurt, <italic...

The theory of multi-adjoint logic programs has been introduced as a unifying framework to deal with uncertainty, imprecise data or incomplete information. From the applicative part, a neural net based implementation of homogeneous propositional multi-adjoint logic programming on the unit interval has been presented elsewhere, but restricted to the case in which the only connectives involved in ...

(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 ...