# physical significance of membership function greater than one

In fuzzy logic, when we associate an element with a set, we usually do it in terms of membership grade which suggests the "belonging" of this element to the set. Membership grade value 0 means that the element is certainly not the set member while grade value = 1 means that the element is definitely a part of the set. In some problems that I was solving, I came across membership grade values of some elements greater than 1. What does it actually mean?

• Please give a reference to where you read that. – Raphael Aug 13 '16 at 16:10
• fuzzy logic can be done in any lattice: grades of membership are elements of the lattice, with the bottom element denoting complete non-membership while the top element denotes certain membership. In your case where the grade is larger than 1, it may be that the the lattice for the fuzzy logic is not [0,1] but some other interval [a,b] ---all such intervals are bounded lattices. Hope this helps! – Musa Al-hassy Aug 15 '16 at 4:26
• I read this in a book on soft computing written by sivandanam and deepa – Upendra Pratap Singh Aug 15 '16 at 15:22