Operations on Zadeh's Z-numbers

The computational technique is explained and examples how sum and product of Z-valuations can be computed are illustrated with examples.

Abstract

Zadeh defined a Z-number associated with an uncertain variable X as an ordered pair of fuzzy numbers,(A,B). The first component represents the value of the variable while the second component gives a measure of certainty. Computations with Z-numbers is a topic which is both interesting and useful. In this paper we explain the computational technique and illustrate with examples how sum and product of Z-valuations can be computed. Keyword: Fuzzy event probability ,Restriction, Zadeh's Z-numbers ,Z-valuation