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.6653943832-559362018-09-05T03:06:04Z Membership functions representing a number vs. representing a set: Proof of unique reconstruction Hung T. Nguyen Vladik Kreinovich Olga Kosheleva Mathematics © 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). 2018-09-05T03:06:04Z 2018-09-05T03:06:04Z 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/6653943832/55936 |
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Mathematics Hung T. Nguyen Vladik Kreinovich Olga Kosheleva Membership functions representing a number vs. representing a set: Proof of unique reconstruction |
| description |
© 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 |
Hung T. Nguyen Vladik Kreinovich Olga Kosheleva |
| author_facet |
Hung T. Nguyen Vladik Kreinovich Olga Kosheleva |
| author_sort |
Hung T. Nguyen |
| 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 |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006725079&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55936 |
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