Abstract
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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Acknowledgments
We acknowledge the partial support of the Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Thailand. This work was also supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.
The authors are thankful to all the participants of the 2016 IEEE World Congress on Computational Intelligence WCCI’2016 (Vancouver, Canada, July 24–29, 2016) for valuable discussions.
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Kreinovich, V., Sriboonchitta, S. (2017). For Multi-interval-valued Fuzzy Sets, Centroid Defuzzification Is Equivalent to Defuzzifying Its Interval Hull: A Theorem. In: Sidorov, G., Herrera-Alcántara, O. (eds) Advances in Computational Intelligence. MICAI 2016. Lecture Notes in Computer Science(), vol 10061. Springer, Cham. https://doi.org/10.1007/978-3-319-62434-1_17
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DOI: https://doi.org/10.1007/978-3-319-62434-1_17
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