The dual modular propinquity is a complete metric, up to full quantum isometry, on the class metrical vector bundles, i.e. of Hilbert modules endowed with type densely defined norm, called D-norm, which generalize operator norm given by connection Riemannian manifold. weaker than yet it complete, main purpose its introduction.

In this paper we generalize the well known construction of ”classic” measure theory to the fuzzy case. We consider such T-norm based classes of fuzzy sets as T-semirings and T-tribes (T sigmaalgebras), such fuzzy valued functions as elementary T-measures, exterior T-measures and T-measures, and we suggest the construction of a TM-measure by extension of an elementary TM-measure on a TM-semiring...

One of the difficulties in building consistent databases comes from mismatches between two digital maps. They are caused by the diversity of database providers and the methodology of map production. Rubber sheeting is one of crucial problems in Geographical Information System, which is a mapping procedure to resolve mismatches between two geographical maps representing the same region with a fe...

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

There is given an axiomatization of the hybrid probabilistic-possibilistic mixture, based on a pair of t-conorm S and t-norm T satisfying (CD) condition, and the corresponding S-measure.