A Note on Z-numbers

  • Authors:
  • Lotfi A. Zadeh

  • Affiliations:
  • Department of EECS, University of California, Berkeley, CA 94720-1776, United States

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

Quantified Score

Hi-index 0.07

Visualization

Abstract

Decisions are based on information. To be useful, information must be reliable. Basically, the concept of a Z-number relates to the issue of reliability of information. A Z-number, Z, has two components, Z=(A,B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. Typically, A and B are described in a natural language. Example: (about 45min, very sure). An important issue relates to computation with Z-numbers. Examples: What is the sum of (about 45min, very sure) and (about 30min, sure)? What is the square root of (approximately 100, likely)? Computation with Z-numbers falls within the province of Computing with Words (CW or CWW). In this note, the concept of a Z-number is introduced and methods of computation with Z-numbers are outlined. The concept of a Z-number has a potential for many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation and rule-based characterization of imprecise functions and relations.