The introduction and the development of the web 2.0 technologies have facilitated
the collaboration between the departments of a company or between companies. This implies that
about agile businesses should be able to adapt too many situations and to choose optimal solutions. In
this context one can take into account the process of building teams of experts regardless of the
location that should solve certain tasks. However, it can be considered that building teams means
putting together different characters, temperaments and cultures and this process is not always
successful. For this reason the purpose of this paper is to describe an evaluation model of the
satisfaction level of the agile teamwork members and implicitly of the companies involved. This
research is using the heterogeneous algebras theory for defining a solution for the reunion of a team of
individuals such as the team should achieve optimal performance levels. As a result, the paper presents
a set of rules that should be fulfilled in order to create an efficient team. This research will be helpful
for the implementation of the main engine of a tool that can be used for building agile teamwork.
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