How to transform partial order between degrees into numerical values

Abstract

Fuzzy techniques are a successful way to handle expert knowledge, enabling us to capture different degrees of experts' certainty in their statements. To use fuzzy techniques, we need to describe experts' degrees of certainty in numerical terms. Some experts can provide such numbers, but others can only describe their degrees by using natural-language words like “very”, “somewhat”, “to some extent”, etc. In general, all we know about these word-valued degrees is that there is a natural partial order between these degrees: e.g., “very small” is clearly smaller than “somewhat small”. In this paper, we propose a natural way to transform such a partial order between degrees into numerical values.