Affiliations: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China
Correspondence:
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Corresponding author. F.-G. Shi, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. E-mail: [email protected]
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 LX-fuzzy set on E, and it can also be regarded as an LE-fuzzy set on X. Moreover an LE-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 2E-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.
Keywords: L-fuzzy set, L-fuzzy soft set, soft set, fuzzy set of type 2, complete lattice isomorphism
