Fuzzy relational compositions based on grouping features

Abstract

Fuzzy relational compositions play a crucial role in fundamentals of fuzzy mathematics as well as in distinct application areas. Recent studies introduce distinct generalizations, e.g., incorporation of excluding features or the use of generalized quantifiers. No matter the huge positive potential of these approaches, we demonstrate on a real example, that some limitations even for these extensions may be encountered if the features are constructed in a certain specific yet very natural way. However, these limitations can be overcome by a further improvement if a sort of grouping of features is applied. In particular, we study the compositions of fuzzy relations based on partitioned universe of features and then the combination of both above mentioned extensions will be applied and experimentally validated. The results are compared to the original ones provided in the investigation of excluding features without any implementation of generalized quantifiers nor with grouping of the features.