The theory of symmetry of the real crystal gives rise to new generalizations of classical symmetry: the Shubnikov antisymmetry [1], the multiple antisymmetry of Zamorzaev [2], the Belov’s color symmetry [3], the Zamorzaev’s P-symmetry [4], the P-symmetry [5], the Wp-symmetry [6,7], the Wq-symmetry [8-10]. In this paper we discuss the essence of the mixed transformations of a geometric figure, regularly weighted by ”physical” scalar or oriented tasks (compare to [11,12]). In accordance with global nature or local nature of the rule for transformation of ”indexes”, ascribed to each point of the geometric analyzed figure, four types of mixed transformations are obtained. Are determined the conditions in which one mixed transformation is exactly transformation of P-symmetry, or exactly transformation of Wp-symmetry (the broadest generalization of classical symmetry when the ”indexes”-qualities have a scalar character). Moreover, when one mixed transformation is exactly transformation of P-symmetry (Q-symmetry), or exactly transformation of Wq-symmetry (the widest generalization of classical symmetry when the qualities, located in the points of the figure, are homogeneous and with different orientations) . Some properties of the groups of Wp-symmetry and of the groups of Wq-symmetry are studied.