Fuzzy scoring theory applied to team-peer assessment: additive vs. multiplicative scoring models on the signed or unsigned unit interval

Teamwork in educational settings for learning and assessment has a long tradition. The reasons, goals and methods for introducing teamwork in courses may vary substantially. However, in the end, teamwork must be assessed at the group level as well as on the student level. The lecturer must be able to give students credit points or formal grades for their joint output (product) as well as for their cooperation in the team (process). Schemes for such multicriteria quantitative assessments appear difficult to define in a plausible way. Over the last five decades, plenty proposals for assessing teamwork processes and products on team and student level have been given using diverse scoring schemes. There is a broad field of empirical research and practical advice about how team-based educational assessment might be set up, implemented, improved, and accepted by staff and students. However, the underlying methodological problems with respect to the merging of several independent measurements has been severely underestimated. Here, we offer an entirely new paradigm and taxonomy of teamwork-based assessment following a rigorous fuzzy-algebraic approach based on two core notions: quasi-arithmetic means, and split-join-invariance. We will show how our novel approach solves the problem of team-peer-assessment by means of appropriate software tools.