Membership functions representing a number vs. representing a set: Proof of unique reconstruction | IEEE Conference Publication | IEEE Xplore

Membership functions representing a number vs. representing a set: Proof of unique reconstruction


Abstract:

In some cases, a membership function μ(x) represents an unknown number, but in many other cases, it represents an unknown crisp set. In this case, for each crisp set S, w...Show More

Abstract:

In some cases, a membership function μ(x) represents an unknown number, but in many other cases, it represents an unknown crisp set. In this case, for each crisp set S, we can estimate the degree μ(S) to which this set S is the desired one. A natural question is: once we know the values μ(S) corresponding to all possible crisp sets S, can we reconstruct the original membership function? In this paper, we show that the original membership function μ(x) can indeed be uniquely reconstructed from the values μ(S).
Date of Conference: 24-29 July 2016
Date Added to IEEE Xplore: 10 November 2016
ISBN Information:
Conference Location: Vancouver, BC, Canada

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