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http://dx.doi.org/10.5391/IJFIS.2013.13.3.215

Weak laws of large numbers for weighted sums of Banach space valued fuzzy random variables  

Kim, Yun Kyong (Department of Information & Communication Engineering, Dongshin University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.13, no.3, 2013 , pp. 215-223 More about this Journal
Abstract
In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.
Keywords
Fuzzy sets; Random sets; Fuzzy random variables; Weak law of large numbers; Compactly uniform integrability; Tightness; Weighted sum;
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