Preservation of Graded Properties of Fuzzy Relations by Aggregation Functions

13 years 5 months ago

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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.

Urszula Dudziak

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