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Relational compositions in fuzzy class theory. (English) Zbl 1185.03079
The paper gives a unified, yet elementary, treatment of fuzzy relation theory. The formal background is the fuzzy class theory as conceived by L. Běhounek and P. Cintula [Fuzzy Sets Syst. 154, No. 1, 34–55 (2005; Zbl 1086.03043)], and developed within the framework of the mathematical fuzzy logic \(\mathrm{MTL}_{\triangle}\).
This paper treats a series of notions related to relation composition, like different composition operations, images and preimages. That this elementary treatment is possible shows that the chosen framework is well suited to do, in a serious way, fuzzy mathematics within this framework.

MSC:
03E72 Theory of fuzzy sets, etc.
03E70 Nonclassical and second-order set theories
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