For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem
© Springer International Publishing AG 2017. In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed t...
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th-cmuir.6653943832-410332017-09-28T04:15:10Z For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem Kreinovich V. Sriboonchitta S. © Springer International Publishing AG 2017. In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull. As a consequence of this result, we prove that the centroid defuzzification of a general type-2 fuzzy set can be reduced to the easier-to-compute case when for each x, the corresponding fuzzy degree of membership is convex. 2017-09-28T04:15:10Z 2017-09-28T04:15:10Z 2017-01-01 Book Series 03029743 2-s2.0-85028459632 10.1007/978-3-319-62434-1_17 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85028459632&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41033 |
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© Springer International Publishing AG 2017. In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull. As a consequence of this result, we prove that the centroid defuzzification of a general type-2 fuzzy set can be reduced to the easier-to-compute case when for each x, the corresponding fuzzy degree of membership is convex. |
| format |
Book Series |
| author |
Kreinovich V. Sriboonchitta S. |
| spellingShingle |
Kreinovich V. Sriboonchitta S. For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| author_facet |
Kreinovich V. Sriboonchitta S. |
| author_sort |
Kreinovich V. |
| title |
For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| title_short |
For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| title_full |
For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| title_fullStr |
For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| title_full_unstemmed |
For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem |
| title_sort |
for multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: a theorem |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85028459632&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41033 |
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