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The goal of this dissertation is to extend the concept of the reducibility
in a hypergroup to the fuzzy case, by defining a fuzzy reduced hypergroup, i.e., a crisp hypergroup endowed with a fuzzy set which is reduced. Moreover, we intend to extend the concept of reducibility to the hyperrings, also, in the crisp case. Using these concepts, we aim to study the reducibility and the fuzzy reducibility in algebraic hyperstructures, especially in hypergroups and hyperrings.
Cilj ove disertacije je ekstenzija koncepta reducibilnosti u hipergrupama na
fazi slučaj, definisanjem fazi reducibilne hipergrupe tj. klasične hipergrupe obogačene sa fazi skupom koja je reducibilna. Osim toga, namjeravamo da prosirimo koncept reducibilnosti na hiperprstene, takođe, u klasicnom slucaju. Koriste^i ove koncepte, nas cilj je da proucavamo svojstvo reducibilnosti (u klasicnom i fazi slucaju) u algebarskim hiperstrukturama, posebno u hipergrupama i hiperprstenima.
Reducibility, hyperstructures, equivalence relations, fundamental relations, fuzzy reducibility
The goal of this dissertation is to extend the concept of the reducibility
in a hypergroup to the fuzzy case, by defining a fuzzy reduced hypergroup, i.e., a crisp hypergroup endowed with a fuzzy set which is reduced. Moreover, we intend to extend the concept of reducibility to the hyperrings, also, in the crisp case. Using these concepts, we aim to study the reducibility and the fuzzy reducibility in algebraic hyperstructures, especially in hypergroups and hyperrings.