Weighted fuzzy averages in fuzzy environment: part I. Insufficient expert data and fuzzy averages

  • 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

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Abstract

Three new versions of the most typical value (MTV)1,2 of the population (generalized weighted averages) are introduced. The first version, WFEVg, is a generalization of the weighted fuzzy expected value (WFEV)3 for any fuzzy measure g on a finite set and it coincides with the WFEV when a sampling probability distribution is used. The second and the third version are respectively the weighted fuzzy expected intervals WFEI and WFEIg which are generalizations of the WFEV, namely, MTVs of the population for a sampling distribution and for any fuzzy measure g on a finite set, respectively, when the fuzzy expected interval (FEI)4 exists but the fuzzy expected value (FEV)4 does not. The construction process is based on the Friedman-Schneider-Kandel (FSK)3 principle and results in the new MTVs called the WFEI and the WFEIg when the combinatorial interval extension of a function5 is used.