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On fuzzy \(\Lambda_\gamma \)-sets and their applications. (English) Zbl 1444.54004

Summary: The notion of \(\Lambda \)-fuzzy set was introduced by M. E. El-Shafei and A. Zakari [Arab. J. Sci. Eng., Sect. A, Sci. 31, No. 2, 197–206 (2006; Zbl 1184.54008)]. We examine some basic properties of it and prove some characterization theorems for the same. The paper presents a new class of fuzzy sets called fuzzy \(\Lambda_\gamma \)-sets that includes the class of all fuzzy \(\gamma \)-open sets. It also introduces the notion of fuzzy \(V_\gamma \)-sets as the dual concept of fuzzy \(\Lambda_\gamma\) sets to study the spaces constituted by those sets and obtain a completely different structure which is called fuzzy independent Alexandorff space. A stronger form of fuzzy \(\Lambda_b\)-continuity. G. Aslım and G. Günel [Chaos Solitons Fractals 42, No. 2, 1024–1030 (2009; Zbl 1198.54007)] called fuzzy \(\Lambda_\gamma \)-continuity is introduced and the relationships are also established with the already existing functions accordingly. Finally, fuzzy \(\Lambda_\gamma \)-Generalized closed sets are defined and studied with some of their applications.

MSC:

54A40 Fuzzy topology
03E72 Theory of fuzzy sets, etc.
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