Composition Models of Fuzzy Relations Considering Importance Levels of Features*

Severa1 fuzzy concepts are involved in relational databases such as the degree of fulfilment of a graded property, the level of importance (or of possibility) of a component in a query, grouping features, or the concept of fuzzy quantifiers. We have recently approached the concepts of excluding features and unavoidable features to construct the extensions of fuzzy relational compositions. The extended compositions include the employment of fuzzy quantifiers as well. In this work, we approach the concept of importance levels of considered features in a particular sense that is intuitively suitable to the classification tasks. Then we propose a direction of incorporating this concept into the existing fuzzy relational compositions. We provide various useful properties related to the new models of the compositions. Furthermore, a simple example of the classification of animals in biology is addressed for the behaviour illustration of the proposed models. Finally, we examine the applicability of the new models to the practical application of the Dragonfly classification, which has been considered previously.