How to Transform Partial Order Between Degrees into Numerical Values

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Joe Lorkowski, The University of Texas at El PasoFollow
Martha Osegueda Escobar, The University of Texas at El PasoFollow

Publication Date

6-2016

Comments

Technical Report: UTEP-CS-16-22a

To appear in Proceedings of International IEEE Conference on Systems, Man, and Cybernetics SMC'2016, Budapest, Hungary, October 9-12, 2016.

Abstract

Fuzzy techniques are a successful way to handle expert knowledge, enabling us to capture different degrees of expert's certainty in their statements. To use fuzzy techniques, we need to describe expert's degree 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.