Properties of fuzzy relations and aggregation process in decision making

Document Type : Research Paper


Interdisciplinary Centre for Computational Modelling, University of Rzeszow, Al. Rejtana 16C, 35-959 Rzeszow, Poland


In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relation
RF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzy
relation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relations
R1, . . . ,Rn is examined. Here, it is considered the converse approach. Namely, fuzzy relation RF = F(R1, . . . ,Rn) is
assumed to have a given property and then it is checked if fuzzy relations R1, . . . ,Rn have this property. Moreover, a
discussion on the mentioned two approaches is provided. The properties, which are examined in this paper, depend on
their notions on binary operations B : [0, 1]2 → [0, 1]. By incorporating operation B these properties are generalized
versions of known properties of fuzzy relations.


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