Restored fuzzy measures in expert decision-making

  • Authors:

  • G. Sirbiladze;T. Gachechiladze

  • Affiliations:

  • Department of Applied Mathematics and Computer Sciences, I, Javakhishvili Tbilisi State University, 2 University Street, Tbilisi 0143, Georgia;Department of Applied Mathematics and Computer Sciences, I, Javakhishvili Tbilisi State University, 2 University Street, Tbilisi 0143, Georgia

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2005

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Abstract

The paper deals with problems of fuzzy measure restoration from insufficient data on a finite set. The proposed approach is constructed in the class of second order Choquct capacities [Fuzzy Sets and Systems 31 (1989) 23; Reports of the Enlarged Session of I. Vekua Inst. Appl. Math. 14 (1999) 31; Ann. Inst. Fourier 5 (1953) 131] when "the fuzzy weights" of singletons are known. This essentially concerns certain frequency distributions, where the nature of additivity is doubtful because of the fuzzy nature of data distribution. This is the indisputable condition for the introduction of a fuzzy measure, but the insufficient one for its construction.Measures of specificity, indices of uncertainty and estimators of approximations are calculated. Some approximation properties are proved. Using the approach of A. Kaufman's experton theory [Les expertons, Hermes, Paris, 1987], the unique fuzzy subset (fuzzy object) is constructed from the associated probabilities [Fuzzy Sets and Systems 31 (1989) 23] of the restored fuzzy measure.The application of the constructed method is illustrated by an example of the processing of certain insufficient statistical data of the Georgian language. As a result, it becomes possible to derive estimates for the Georgian language on the whole.