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Fuzzy soft sets as L -fuzzy sets

Authors: Fu-Gui Shi; Chao-Zan Fan;

Fuzzy soft sets as L -fuzzy sets

Abstract

In this paper, it is shown that an L -fuzzy soft set on X with a set E of parameters can be regarded as an L X -fuzzy set on E , and it can also be regarded as an L E -fuzzy set on X . Moreover an L E -fuzzy set on X can also be regarded as an L -fuzzy sets on E × X . In particular, a soft set on X with a set E of parameters actually can be regarded as a 2 E -fuzzy set or a crisp subset of E × X . This shows that the concept of (fuzzy) soft set is redundant. Further it is shown that the notions of soft groups, soft rings and fuzzy soft semigroups are respectively special cases of the corresponding L -fuzzy groups, L -fuzzy rings and L -fuzzy semigroups. Therefore, theoretical workers should stop working in these restrictive and complicated programs, while applied workers should transfer the need or appropriateness of (fuzzy) soft set notions to lattice-valued fuzzy sets or fuzzy sets of type 2.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Average
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