{'fraction_non_alphanumeric': 0.05370101596516691, 'fraction_numerical': 0.002902757619738752, 'mean_word_length': 5.571428571428571, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Preservation of Graded Properties of Fuzzy Relations by Aggregation Functions

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties, e.g. an α–equivalence, α–orders. Using functions of n variables we consider aggregation fuzzy relation of given fuzzy relations. We give conditions for functions to preserve graded properties of fuzzy relations.