Membership functions representing a number vs. representing a set: Proof of unique reconstruction
© 2016 IEEE. 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...
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th-cmuir.6653943832-413482017-09-28T04:20:51Z Membership functions representing a number vs. representing a set: Proof of unique reconstruction Nguyen H. Kreinovich V. Kosheleva O. © 2016 IEEE. 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). 2017-09-28T04:20:51Z 2017-09-28T04:20:51Z 2016-11-07 Conference Proceeding 2-s2.0-85006725079 10.1109/FUZZ-IEEE.2016.7737749 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006725079&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41348 |
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© 2016 IEEE. 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). |
| format |
Conference Proceeding |
| author |
Nguyen H. Kreinovich V. Kosheleva O. |
| spellingShingle |
Nguyen H. Kreinovich V. Kosheleva O. Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| author_facet |
Nguyen H. Kreinovich V. Kosheleva O. |
| author_sort |
Nguyen H. |
| title |
Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| title_short |
Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| title_full |
Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| title_fullStr |
Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| title_full_unstemmed |
Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| title_sort |
membership functions representing a number vs. representing a set: proof of unique reconstruction |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006725079&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41348 |
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1681421985532346368 |