A new approach to representing and defuzzifying a Z-number and Z-valuation

The concepts of Z-number and Z-valuation were introduced by Zadeh in 2011. Z-number is an ordered pair (A, B) while a Z-valuation is an ordered triple (X, A, B) that indicates it is equal to the assignment statement variable X is (A, B). In this paper, with the consideration of thinking uncertainty, the second component B of Z-number towards the first component A of Z-number is regarded as the uncertain region of the fuzzy number. Base on this understanding, the paper discussed the approach to converting from a Z-number to a crisp number. First the fuzzy number of A is converted to an interval-valued fuzzy set with footprint of uncertainty (FOU). Then, by computing the centroid of the interval-valued fuzzy set with K-M algorithm, the Z-number is converted to a crisp number which can be used for decision making.