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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| Main Authors: | , |
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| Format: | Book Series |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85028459632&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/46738 |
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| Institution: | Chiang Mai University |
| Summary: | © 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. |
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