Abstract: The recently defined concept of statistical depth function for fuzzy sets provides a theoretical framework for ordering fuzzy sets with respect to the distribution of a fuzzy random variable. One of the most used and studied statistical depth functions for multivariate data is simplicial depth, based on multivariate simplices. We introduce a notion of pseudosimplices generated by fuzzy sets and propose three generalizations of simplicial depth to fuzzy sets. Their theoretical properties are analyzed and the behavior of the proposals is illustrated through a study of both synthetic and real data.

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