University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416320190629Properties of fuzzy relations and aggregation process in decision making115464010.22111/ijfs.2019.4640ENU.BentkowskaInterdisciplinary Centre for Computational Modelling, University of Rzeszow, Al. Rejtana 16C, 35-959 Rzeszow, PolandJournal Article20170713In this contribution connections between input fuzzy relations R<sub>1</sub>, . . . ,R<sub>n</sub> on a set <em>X</em> and the output fuzzy relation<br />R<sub>F</sub> = F(R<sub>1</sub>, . . . ,R<sub>n</sub>) are studied. F is a function of the form F : [0, 1]<sup>n</sup> → [0, 1] and R<sub>F</sub> is called an aggregated fuzzy<br />relation. In the literature the problem of preservation, by a function <em>F</em>, diverse types of properties of fuzzy relations<br />R<sub>1</sub>, . . . ,R<sub>n</sub> is examined. Here, it is considered the converse approach. Namely, fuzzy relation R<sub>F</sub> = F(R<sub>1</sub>, . . . ,R<sub>n</sub>) is<br />assumed to have a given property and then it is checked if fuzzy relations R<sub>1</sub>, . . . ,R<sub>n</sub> have this property. Moreover, a<br />discussion on the mentioned two approaches is provided. The properties, which are examined in this paper, depend on<br />their notions on binary operations B : [0, 1]<sup>2</sup> → [0, 1]. By incorporating operation B these properties are generalized<br />versions of known properties of fuzzy relations.http://ijfs.usb.ac.ir/article_4640_dc4adb5c9a4cc97602f04fd3e6fcdcb3.pdf