Abstract

SANCHEZ-LARIOS, H.  and  GUILLEN-BURGUETE, S.. A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rⁿ. J. appl. res. technol [online]. 2010, vol.8, n.3, pp.416-424. ISSN 2448-6736.

In this paper, we give theoretical foundations for modeling distance functions on the usual Euclidean space Rⁿ, where distance may refer to physical kilometers, liters of fuel consumed, time spent in traveling, or transportation cost. In our approach, a distance function d is derived from a function F₀ called the fundamental function of d. Our distance functions, unlike metrics, can be asymmetric and non-positive definite, and unlike the Lp norms, they can be nonuniform. We illustrate our theoretical framework by modeling an asymmetric and non-uniform distance function on R² which can take negative values.

Keywords : Distance function; isotropy; non-uniformity; asymmetry; weighted Lp-norm.

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