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A perspective on the extension of stochastic orderings to fuzzy random variables

Abstract : In this paper we study how to make joint extensions of stochastic orderings and interval orderings so as to extend methods for comparing random variables, from the point of view of their respective location or magnitude, to fuzzy random variables. The main idea is that the way fuzzy random variables are interpreted affects the choice of the comparison methods. We distinguish three views of fuzzy random variables, according to which various comparison methods seem to make sense. This paper offers an approach toward a systematic classification of combinations of stochastic and interval or fuzzy interval comparison methods.
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Ines Couso, Didier Dubois. A perspective on the extension of stochastic orderings to fuzzy random variables. 16th International Fuzzy Systems Association World Congress and 9th Conference of the European Society for Fuzzy Logic and Technology (IFSA - EUSFLAT 2015), Jun 2015, Gijon, Spain. pp.1486-1492, ⟨10.2991/ifsa-eusflat-15.2015.211⟩. ⟨hal-01290482⟩

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