The Maximal Variance of Fuzzy Interval
نویسنده
چکیده
There is a well-known interpretation of fuzzy interval in the framework of the theory of imprecise probabilities [1, 2]. To get this, we associate with any fuzzy interval a possibility or necessity measure, and then consider that values of the pointed measures give us lower or upper assessments of probabilities. This interpretation was discussed in detail in [3], and there it is proposed to use upper and lower expectations for evaluating uncertainty of such intervals. These characteristics and other crude moments of order k can be easily calculated by Choquet integral. However, to calculate upper and lower central moments is more difficult as it is shown in investigations, presented below. Throughout the paper we will use the following notations: 1) E [ξ] is an or-
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