Revistes Catalanes amb Accés Obert (RACO)

The distribution of mathematical expectations of a randomized fuzzy variable

V. B. Kuz'min, S.I. Travkin


The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables.

We show that this distribution has a specific analytical structure and may be represented by means of Wan-der-Mond determinant derivatives. The relation between the notions of expectations of fuzzy variables and the Pareto optimality is demonstrated.

The mathematical expectation of the upper and lower expected values of a randomized fuzzy variable and their asymptotics are calculated.

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