Possibility and Gradual Number Approaches to Ranking Methods for Random Fuzzy Intervals

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This paper deals with methods for ranking fuzzy intervals in connection with probabilistic and interval orderings. According to the interpretation of a fuzzy interval, various such extensions can be laid bare. In this paper, we especially consider extensions of probabilistic orderings using possibilistic interpretations of fuzzy intervals, crisp substitutes thereof, and gradual numbers. This framework can encompass the comparison of fuzzy random variables: coupling one form of probabilistic comparison with one form of interval comparison induces a method for ranking random fuzzy intervals.