In the paper the problem of preservation of properties of fuzzy relations during aggregation process is considered. It means that properties of fuzzy relations R1, . . . ,Rn on a set X are compared with properties of the aggregated fuzzy relation RF = F(R1, . . . ,Rn), where F is a function of the type F : [0, 1]n → [0, 1]. There are discussed α-properties (which may be called graded properties) as reflexivity, irreflexivity, symmetry, asymmetry, antisymmetry, connectedness and transitivity, where α ∈ [0, 1]. Fuzzy relations with a given graded property are considered (there may be diverse grades of the same property) and the obtained grade of the aggregated fuzzy relation is provided. There is also discussed the ,,converse” problem. Namely, relation RF = F(R1, . . . ,Rn) is assumed to have a graded property and the properties of relations R1, . . . ,Rn are examined (possibly with some assumptions on F).
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.
Oct 15, 2021
Jul 19, 2021