When Should We Switch from Interval-Valued Fuzzy to Full Type-2 Fuzzy (e.g., Gaussian)?

Full type-2 fuzzy techniques provide a more adequate representation of expert knowledge. However, such techniques also require additional computational efforts, so we should only use them if we expect a reasonable improvement in the result of the corresponding data processing. It is therefore important to come up with a practically useful criterion for deciding when we should stay with interval-valued fuzzy and when we should use full type-2 fuzzy techniques. Such a criterion is proposed in this paper. We also analyze how many experts we need to ask to come up with a reasonable description of expert uncertainty. 1 Formulation of the Problem Need for fuzzy logic. In many application areas, we have expert knowledge formulated by using imprecise (“fuzzy”) words from natural language, such as “small”, “weak”, etc. To use this knowledge in automated systems, it is necessary to reformulate it in precise computer-understandable terms. The need for such a reformulation was one of the motivations behind fuzzy logic (see, e.g., [3, 11, 15]). Fuzzy logic uses the fact that in a computer, “absolutely true” is usually represented as 1, and “absolutely false” is represented as 0. Thus, to describe expert’s intermediate degrees of confidence, it makes sense to use real numbers intermediate between 0 and 1.