Classical and Fuzzy Neighborhood Relations of the Temporal Qualitative Algebra

In this paper we study the problem of representing different forms of imperfect temporal knowledge. Imperfection in knowledge can be present in the forms of coarse knowledge about temporal events or even in the form of incomplete, imprecise, vague or uncertain temporal information. The two orthogonal notions of coarseness and fuzziness seem to be quite adequate to manage these two kinds of temporal ignorance and they can be combined to develop a more general model. The first part of the present study is dedicated to the definition of a new Neighborhood Temporal Qualitative Algebra nQA starting from Freksa´s work about Allen´s Algebra neighborhood relations. Freksa´s Algebra is merged with the Convex Point Algebra and all the neighborhood relations needed to close the nQA Algebra are computed automatically. The Algebra nQA is tractable. In the second part of the paper, the fuzziness notion is considered and combined with that of conceptual neighborhood. The algebra nQA^fuz is defined as a fuzzy extension of the algebra nQA, and the conditions of its tractability are studied.