Weighted fuzzy averages in fuzzy environment: part II. Generalized weighted fuzzy expected values in fuzzy environment

  • Authors:

  • G. Sirbiladze;A. Sikharulidze

  • Affiliations:

  • Chair of Random Precesses Theory, Department of Applied Mathematics and Computer Sciences, Tbilisi State University, Georgia, 2, University St., Tbilisi 380043, Georgia;Chair of Software and Information Technologies, Department of Applied Mathematics and Computer Sciences, Tbilisi State University, Georgia, 2, University St., Tbilisi 380043, Georgia

  • Venue:
  • International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

The weighted fuzzy expected value (WFEV) of the population for a sampling distribution was introduced in. In the notion of WFEV is generalized for any fuzzy measure on a finite set (WFEVg). The latter paper also describes the notions of weighted fuzzy expected intervals WFEI and WFEIg which are an interval extension of WFEV and WFEVg, respectively, when due to "scarce" data the fuzzy expected value (FEV) does not exist, but the fuzzy expected interval (FEI) does. In this paper, The generalizations GWFEVg and GWFEIg of WFEVg and WFEIg, respectively, are introduced for any fuzzy measure space. Furthermore, the generalized weighted fuzzy expected value is expressed in terms of two monotone expectation (ME)4 values with respect to the Lebesgue measure on [0,1]. The convergence of iteration processes is provided by an appropriate choice of a "weight" function. In the interval extension (GWFEIg) the so-called combinatorial interval extension of a function 5 is successfully used, which is clearly illustrated by examples. Several examples of the use of the new weighted averages are discussed. In many cases these averages give better estimations than classical estimators of central tendencies such as mean, median or the fuzzy "classical" estimators FEV, FEI and ME.