A Constrained Parametric Approach for Modeling Uncertain Data

Data obtained from the real-world tends to be uncertain: Measurement inaccuracies, variability in opinions, and human errors are just some of the reasons that make the information collection process noisy. In recent years, fuzzy sets have been used to capture the uncertainty in data and then build automatic reasoning systems. In some contexts, data on a given subject is gathered from multiple sources and each instance modeled through a fuzzy set. A typical example of this scenario is represented by surveys, in which many participants express their opinions on the same topics. The fuzzy sets representing individual instances can be combined in a new (type-1 or type-2) fuzzy set in order to capture expert or measurement variation. In this article, we propose a novel approach which combines uncertain data modeled through parametric fuzzy sets in an intuitive manner, using the recently introduced constrained interval type-2 (IT2) fuzzy sets . By intuitive, we mean that each resultant constrained IT2 fuzzy set preserves the shape used to represent a single data instance, while making use of the footprint of uncertainty to represent uncertainty around its parameters. This novel constrained parametric approach is applied to interval-valued data gathered from real surveys and compared to the other algorithms in the literature, showing how it differs from them, with discussion of the contexts in which it represents a valuable alternative. Finally, it is shown how this novel approach can be used to model not just intervals but data in which individual instances can be modeled through any parametric fuzzy sets (e.g., triangular).