A methodology for controlling the information quality in interval-valued fusion processes: Theory and application

An important problem faced when dealing with imperfect information in fusion processes the uncertainty regarding values of the membership degrees to be employed in fuzzy modeling. In this scenario, one can apply interval-valued (iv) fuzzy sets, in which the membership degrees are represented by intervals. A recurrent issue is the situation in which the quality of information carried by the intervals, expressed by their widths, suffers degradation during the fusion process. So, the main objective of this paper is to develop a general framework to construct iv-fusion functions whose outputs conserve the information quality of the operated intervals. To achieve that, first, extend important concepts such as width-limiting functions and width-limited iv-functions to the n -dimensional context. Then, we present a characterization for any subclass of increasing fusion function by their set of properties, followed by the interval extension of such characterization to obtain classes of width-limited iv-fusion functions. We show that our methodology is general enough to retrieve several classes of iv-aggregation functions from the literature. Two approaches for constructing width-limited iv-fusion functions are also presented, which enables the application of different subclasses of width-limited iv-fusion functions in fusion/aggregation processes with imperfect information. Finally, we present a case study on a classification problem. Specifically, we use IVTURS, a state-of-the-art iv-fuzzy rule-based classification system, and a particular subclass of width-limited iv-fusion functions ( n -dimensional width-limited iv-overlap functions), showing that the control of the information quality through width limitation significantly enhances the accuracy of the classifier. • Width-limitation on interval fusion functions to conserve the information quality. • General framework for n -dimensional width-limited interval-valued fusion functions. • Construction methods for applicable width-limited interval-valued fusion functions. • Case study in interval-valued fuzzy rule-based classification systems. • Controlling the interval outputs’ widths improves the classification accuracy.