The concept of unavoidable features in fuzzy relational compositions

摘要

Fuzzy relational calculus, and especially, the compositions of fuzzy relations, had a great impact on many theoretical as well as practical areas of fuzzy modeling and it attracted numerous researchers. Recently, the compositions had been extended in distinct directions including the incorporation of excluding features or the direct use of generalized quantifiers instead of the standard ones. This article provides an investigation of an extension that is mathematically similarly constructed to the concept of excluding features although from the semantic point of view it is opposite. In particular, we introduce the concept of unavoidable features. Formally, the concept is again constructed as conjunctive fusion of an existing fuzzy relational composition with another composition, namely the Bandler-Kohout superproduct, employing a newly defined fuzzy relation of unavoidable features for particular classes. We provide an investigation of mathematical properties of the new concept and we demonstrate the appropriateness of the proposed concept on the classification task. This is provided with help of a real biological classification problems running on a data-sets of dragonflies and amphibians. A significant improvement of the results is emphasizing how strong influence may be provided with simple ideas and concepts fused appropriately together to a more complicated yet still explainable concept.