Human centricity in computing with fuzzy sets: an interpretability quest for higher order granular constructs

The intent of this study is to investigate the capabilities of granular computing (and computing with fuzzy sets, in particular) that are available in the currently existing framework to support the design of human-centric systems. Being cognizant of the inherently numeric nature of fuzzy sets (membership functions), we propose several essential enhancements in order to further foster their interpretability capabilities. Type-2 fuzzy sets are discussed in this setting. It is shown that they capture individual fuzzy sets and the result of their aggregation (along with the ensuing diversity) becomes reflected in the higher type of the fuzzy set. Type-2 fuzzy sets can emerge as a result of linguistic interpretation of the original numeric membership grades. The study brings forward a detailed algorithmic framework leading to the determination of type-2 fuzzy sets: in the case of aggregation, the principle of justifiable granularity is a computational vehicle while in case of linguistic interpretation we introduce a certain optimization scheme minimizing entropy which associates with the interpretation of membership functions through a limited codebook of linguistic labels. The data-driven aspects of information granules are also discussed; here we elaborate on some constructs, which rely on domain knowledge as well as experimental (predominantly numeric) evidence; this concerns both knowledge-based clustering and statistically-inclined logic operators.