WEIGHTED FUZZY AVERAGES IN FUZZY ENVIRONMENT PART II. GENERALIZED WEIGHTED FUZZY EXPECTED VALUES IN FUZZY ENVIRONMENT

摘要

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 (WFEV_g). The latter paper also describes the notions of weighted fuzzy expected intervals WFEI and WFEI_g which are an interval extension of WFEV and WFEV_g, 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 GW FEV_g and GW FEI_g of WFEV_g and WFEI_g, respectively, are introduced for any fuzzy measure space. Furthermore, the generalized weighted fuzzy expected value is expressed in terms of two monotone expectation (ME) 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 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, FBI and ME.