# Similarity Modul

(August 2015)

Often there is the same set of objects however different multi-indicatorsystems available. For instance the multidimensional aspect of poverty of regions on the one side and factors of economical power of these regions on the other side. Hence two partial orders of regions arise. One controlled by poverty and one by economical factors such as innovation potential, level of education, level of technology etc.

Are the two partial orders in conflict to each other, or can a hypothesis derived from the one partial order to explain the other?

The new similarity module of PyHasse is a first attempt to analyse this kind of questions.

Have a look at the documentation and/or calculation of the module.

# Spyout module

(March 2015)

The module spyout, is thought of as an introductory program, making newcomers familiar with some ideas of the theory of partially ordered sets. The module spyout should at best motivate the user to try out the other already existing modules. The module spyout has as usual: Basic information concerning the data matrix (Menue: “Calculate”):

• list of objects
• list of attributes (indicators)
• output of the data matrix

and both important order theoretical matrices the zeta-matrix as well as the cover-matrix. It informs about equivalence classes and its representative elements. Furthermore a Hasse diagram can be obtained with all its facilities (zooming, downsets, upsets, local Hasse diagram incomparables).

So far, spyout provides the same basic information pieces as any other module of PyHasse.

• Basic statistics of the data matrix for each indicator: When the user want to get more information in that context, other software products could be helpful, for example the free software R.

• Connectivities: Here a list appears, where for each representative element x the number of elements in the

• down set
• upset
• appears together with the number of elements incomparable with x

## Chain list

A connectivity between x and an element z for instance in the down set does not necessarily mean that there is only one path from x to z. Therefore the next step could be to check “chain list”, where all chains are listed, which are possible between x and z, ordered due to decreasing length. A more extensive study of chains can be the next step, especially following the question whether or not chains of the same length are similar. This question can be studied in the module chain.

## Conflicts

No connection between x and an element y: Then y is one of the elements in the set of elements incomparable with x. Then a further study is possible to find out, what are the reasons for the incomparability in terms of the indicator values. I.e. here the the submenu “conflicts” can be helpful. When still more information is wanted then the module acm can be helpful.

Have a look at the documentation and/or calculation of the module.

# Fuzzy module

(February 2015)

Application of fuzzy concepts within the framework of partial orders is one interesting option to take into regard that not any slight numerical difference is considered as relevant for a ranking. Now a fuzzy concept is available within PyHasse.

Have a look at the documentation and/or calculation of the module.