This is an interesting question.

A good introduction to the Tanimoto index is given in

J.R. Davies, Statistical methods for matching protein-ligand binding sites, Ph.D. thesis, University of Leeds, 2009:

https://www1.maths.leeds.ac.uk/statistics/pgstats/theses/davies.pdf

See the origins and definition of the Tanimoto index in Section 1.6.2, starting on page 39.    The Tanimoto index value is a score that obtained by comparing a pair of structures based on the number of fragments (parts) in each structure.    This is quite different from the Euclidean distance, which is a measure of the distance between a pair of points (vectors).    In fact, a Tanimoto index value is a real number.     Tanimoto index values can be compared in terms of the absolute value of the difference between the index values. 

The contrast between the Tanimoto index and Euclidean distance is given in

C. Suenderhauf, In Silico Prediction of Drug Transport Across Physiological Barriers, Ph.D. thesis, Basel University, 2011:

http://edoc.unibas.ch/1384/1/THESIS_CLAUDIA_SUENDERHAUF-2011-09-26.pdf

The Hodgkin measure of geometric similarity is defined as the Tanimoto measure of the volumes in

G. Mate, Graphical and Topological Analysis of the Cell Nucleus, Ph.D. thesis, University of Heidelberg, 2013:

http://archiv.ub.uni-heidelberg.de/volltextserver/16119/1/thesis.pdf

See Section 6.1.1, starting on page 117.

See Table 1, p. 30.   Geometric similarity is defined as the Tanimoto or Jacard measure of the volumes on page 128.

If I do not misunderstand the question, you want to combine two distances (or dissimilarity measures) to obtain a third with better properties. You can do it in a supervised or unsupervised way, depending on the availability of classification labels. You have to look for "distance combination" or "metric combination". The most direct way is to use the Gower distance, that is a liner combination of the involved similarities. Other approaches use semidefinite programming and other optimization techniques. Our approach consists in considering the distance matrices and then combining then to use in classification problems. You can find it in Machine learning 78 (1-2), 137-174, and in the list of publications of my profile.

I need a similarity measure similar to Tanimoto to compare fuzzy fingerprints. Fingerprints of real value elements (not 1 and 0 but say 0.3, 0.7). 

@Ivan Petkov Bangov : I need a similarity measure similar to Tanimoto to compare fuzzy fingerprints.

In the following thesis, there is an interesting approach to fuzzy fingerprints that might help you:

M. Mernberger, Graph-Based Approaches to Protein Structure Comparison--From Local to Global Similarity, Ph.D. thesis, Philipps-Universitaet Marburg, 2011:

http://archiv.ub.uni-marburg.de/diss/z2012/0057/pdf/dmm.pdf

The basic approach to realize a fuzzy fingerprint results from altering the concept of a pattern by replacing edge weights by fuzzy sets (see page 98).    Hopefully, this will lead us in the direction you suggested and give you a useful similarity measure.

Thank you very much James.

Please forgive me for taking so long to reply.

My original idea was to filter natural products from the database that are similar (>0.85 Tanimoto) to a query molecules that are active. The same procedure will be applied with euclidean distance (0 - 1). After, I will visualize the filtered structures that appear in both chemical space. Is it possible? What is the best way to combine two different similarity indices for similarity based virtual screening?

Thank you for all contributions.

Best regards.