If A is a maximal fuzzy set in N(X)( set of normal fuzzy sets on X), is it possible to find a fuzzy set B with A(x)<B(x) for some x in X?

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Jayaram M.A

Yes!

We need to come out with a threshold value for this.

Bhowmik Subrata

It depends how you defining the order relation of normal sets with, if it is the set inclusion relation is the order relation and A not a crisp set/ characteristic function then there exists such B, take a point x such that A(x)

Maha Alghamdi

Yes, the considered order relation is the set inclusion. So in your example, B(x)=r and B(y)=A(y) if y is different from x. Clearly, A is a proper subset of B and B is normal. Hence A is not a maximal. Am I right?!