Combining user´s preferences and quality criteria into a new index for guiding the design of fuzzy systems with a good interpretability-accuracy trade-off

Assessing interpretability of fuzzy systems still remains an open and challenging problem. Defining a good index is extremely difficult mainly due to the inherent subjective nature of interpretability. It strongly depends on the background of the person who makes the assessment according to its own knowledge, but also taking into account its previous experience and preferences. Since looking for fuzzy systems with a good accuracy-interpretability trade-off is required for many applications, guiding the whole design process by a good quality index would be extremely appreciated. Such index must be aware of both accuracy and interpretability. This paper introduces a framework that makes possible defining an index easily adaptable to the context of each problem by means of incorporating user´s preferences and quality criteria. To do so, all aspects related to interpretability are first identified and then combined into a decision hierarchy framework. It is derived from a previous experimental study based on a web poll. The top of the hierarchy represents the quality index while the bottom includes all fuzzy systems to be evaluated. It consists of k decision levels structured as suggested by the classical analytic hierarchy process (AHP) defined by Saaty. In addition, the aggregation process is made using the ordered weighted averaging (OWA) operators defined by Yager. Such AHP+OWA combination was already proposed by Yager for solving multi-criteria decision problems. A simple example shows how the proposed method becomes effective but also efficient when assessing several fuzzy systems in an automatic process. The index is easily adaptable for providing those rankings expected by different users.