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The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers

Łyczkowska-Hanćkowiak A., Piasecki K.

Operations Research and Decisions

2018

Vol. 28, No. 2

41--56

We consider the obvious thesis that the present value of a portfolio is equal to the sum of the present values of its components. The main goal of this paper is the implementation of this thesis in the case when present values are determined by trapezoidal ordered fuzzy numbers. We apply the revised sum of ordered fuzzy numbers. The associativity of such a revised sum is investigated here. In addition, we show that the multiple revised sum of a finite sequence of trapezoidal ordered fuzzy numbers depends on the ordering of its summands. Without any obstacles, the results obtained can be generalized to the case of any ordered fuzzy numbers.

q-analogs of order statistics

Kordecki W., Łyczkowska-Hanćkowiak A.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 2

207--214

We introduce the notion of the q-analog of the k-th order statistics. We give a distribution and asymptotic distributions of q-analogs of the k-th order statistics and the intermediate order statistics with r → ∞ and r − k → ∞ in the projective geometry PG (r − 1; q).