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A fuzzy algebraic system based on the theory of falling shadows. (English) Zbl 0873.08002
Summary: Based on the concept of a falling shadow, a theoretical approach to fuzzy algebraic systems is established. A fuzzy subalgebraic system of an algebraic system is considered as a falling shadow of the “cloud of the subalgebraic systems”. When an algebraic system is a ring, fuzzy subrings (fuzzy ideals, fuzzy prime ideals) of a ring are seen as falling shadows of “the cloud of subrings” (“cloud of ideals”, “cloud of prime ideals”). We show that fuzzy algebraic systems defined by $t$-norms are consequences of our definition under certain conditions.
##### MSC:
 08A99 Universal algebra 20N25 Fuzzy groups