Publication Date




Published in the Proceedings of the Joint 9th World Congress of the International Fuzzy Systems Association and 20th International Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS 2001, Vancouver, Canada, July 25-28, 2001, pp. 1908-1913.


To describe experts' uncertainty in a knowledge-based system, we usually use numbers from the interval [0,1] (subjective probabilities, degrees of certainty, etc.). The most direct way to get these numbers is to ask the expert; however, the expert may not be 100\% certain what exactly number describes his uncertainty; so, we end up with a second-order uncertainty - a degree of certainty describing to what extent a given number d adequately describes the expert's uncertainty about a given statement A. At first glance, it looks like we should not stop at this second order: the expert is probably as uncertain about his second-order degree as about his first-order one, so we need third order, fourth order descriptions, etc. In this paper, we show that from a realistic (granular) viewpoint, taking into consideration that in reality, an expert would best describe his degrees of certainty by a word from a finite set of words, it is sufficient to have a second-order description; from this viewpoint, higher order descriptions can be uniquely reconstructed from the second-order one, and in this sense, the second-order description is sufficient.

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