Computational intelligence

Fuzzy metrics based on generators of Archimedean triangular norms of the class of rational functions

T. M. Ledeneva, T. A. Moiseeva

Voronezh State University, Voronezh, Russia

Abstract: This paper presents the results related to the development of an approach for constructing parametric fuzzy metrics based on additive generators of strict triangular norms from the class of rational functions. The fuzzy metrics were tested on the problem of fuzzy clustering, characterized by the determination of the degree of membership for each object to each cluster, allowing for a more flexible grouping of objects within a given set. The conducted computational experiment convincingly demonstrates the superiority of the new fuzzy metrics compared to the Euclidean metric, taking into account well-known and widely used clustering quality criteria. The fuzzy approach allows “working” with approximate distance values, which is important in the presence of uncertainty, therefore, it can be viewed as an element of intelligent technologies that is advisable to use in the development of information systems for various purposes.

Keywords: triangular norm, additive generator, fuzzy metric, clustering quality criteria.

DOI: 10.14357/20718594240403

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