Associative aggregation functions representing different scale types

In aggregation problems different types of information items can occur. In spite of such diversity, it is possible to reinterpret them approximately in a unique formal setting by means of profiles: an extension of fuzzy set membership functions. Then the original aggregation problem can be modelled by an appropriate profile aggregation. Therefore, in this paper we concentrate on and reconsider some aggregation operators used especially in fuzzy logic. This view is based on the specific role that the same range - the closed unit interval - plays according to different interpretations. On one hand, triangular norms are capable of reflecting the closed unit interval as a negative scale, while triangular conorms interpret it as a positive scale. Both scales are unipolar. On the other hand, uninorms and nullnorms represent a bipolar scale interpretation of the same closed unit interval.