Fuzzy CoCo: Balancing Accuracy and Interpretability of Fuzzy Models by Means of Coevolution

Distinguishability quantification of fuzzy sets

“…As a consequence, most strategies of model building that adopt similarity measures for interpretability enhancement are based on massive search algorithms such as Genetic Algorithms [15,20,23], Evolution Strategies [13], Symbiotic Evolution [11], Coevolution [19], or Multi-Objective Genetic Optimization [12]. Alternatively, distinguishability improvement is realized in a separate design stage, often after some data driven procedure like clustering, in which similar fuzzy sets are usually merged together [17,22].…”

“…[1,5,[9][10][11][12][14][15][16][17]19,20,22,26]). Informally speaking, distinguishability is a relation between fuzzy sets (defined on the same Universe of Discourse) directly related to their overlapping: the more overlapping two fuzzy sets are, the less distinguishable they become.…”

Interpretability constraints for fuzzy information granulation

“…On the semantic level, the normality constraint implies that at least one element of the Universe of Discourse should exhibit full matching with the concept semantically represented by the fuzzy set [54,46,55]. Moreover, in fuzzy sets expressing imprecise quantities, the normality requirement is necessary for modeling existing but not precisely measurable values [56].…”

“…The chosen taxonomy is only one of several possible categorizations. As an example, in [46] a division between ''syntactic" and ''semantic" constraints can be found. Since this work is aimed in analyzing interpretability within the context of granular computing, a different taxonomy has been preferred.…”

Interpretability of Fuzzy Information Granules

“…highly subnormal fuzzy sets). To overcome this problem, in [47] a "default" information granule is used, whose membership function is defined as the complement of the union of all used information granules. In this way, any element not represented by any information granule is covered by this default granule, to which a special action could be attached.…”