Cognitive Representations as Source of Task Conflicts in a Team : Origin and Degrees of Discrepancies

Our paper deals about the analysis of cognitive representation as a source of conflicts between an agent's group and intends to characterize the kind of disagreement that can occur in measurement process face to analyzing a common problem. From this perspective, first of all we study the measurement cognitive process - based on measurement theory - concluding that a topological space is measurable when it is contractible and a continuous map exists. Then we propose topological conditions to the existence of unanimity in measurement. Unanimity in representation - problem space - arises when spaces are homeomorphic and contractible and their measure maps are equal and continuous. Finally, we analyze the discrepancies in measurement and we consider that the failure of unanimity conditions is the origin of disagreement. We study discrepancies in situations when measurement exists and no-measurement exists. In a measurable situation we can get a numerical and real value. In contrast when no-measurement exists we can get a set of values as a result of it. Then we can conclude that two levels of discrepancies exist: - When the measurements are homotopy equivalence as a consequence of first homotopy groups are commutative. - When the measures are not homotopy equivalence as a consequence of first homotopy groups are not commutative. In this case we get non-comparable and incompatible measures