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Fuzzy Random Variables à la Kruse & Meyer and à la Puri & Ralescu: Key Differences and Coincidences

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Frontiers in Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 739))

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Abstract

The concept of the so-called fuzzy random variables has been introduced in the literature aiming to model random mechanisms ‘producing’ fuzzy values. However, the best known approaches (namely, the one by Kwakernaak-Kruse and Meyer and the one by Féron-Puri and Ralescu) have been thought to deal with two different situations and, to a great extent, with two different probabilistic and statistical targets. This contribution highlights some of the most remarkable differences and coincidences between the two approaches.

The author is deeply indebted to the Editors of this book because of inviting her to contribute to this tribute to Professor Rudolf Kruse. I admire Kruse a lot, and as I was invited two decades ago by Roman Slowinski, Didier Dubois and Henri Prade to coauthor with him and Jörg Gebhardt a book chapter, it was a dream that came true. Since then, I have had chance to share meetings, conferences, scientific discussions, editing a special issue, and to have him invited to our university and to Asturias for different commitments. I am delighted for having now the opportunity of saying that all this has been a great privilege for me.

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Acknowledgements

The research in this paper has been partially supported by the Principality of Asturias/FEDER Grant GRUPIN14-101 and the Spanish Ministry of Economy and Competitiveness Grant MTM2015-63971-P. Their financial support is gratefully acknowledged.

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Correspondence to María Ángeles Gil .

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Ángeles Gil, M. (2018). Fuzzy Random Variables à la Kruse & Meyer and à la Puri & Ralescu: Key Differences and Coincidences. In: Mostaghim, S., Nürnberger, A., Borgelt, C. (eds) Frontiers in Computational Intelligence. Studies in Computational Intelligence, vol 739. Springer, Cham. https://doi.org/10.1007/978-3-319-67789-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-67789-7_2

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