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Abstract

We first recall the concept of Z-numbers introduced by Zadeh. These objects consist of an ordered pair (A, B) of fuzzy numbers. We then use these Z-numbers to provide information about an uncertain variable V in the form of a Z-valuation, which expresses the knowledge that the probability that V is A is equal to B. We show that these Z-valuations essentially induce a possibility distribution over probability distributions associated with V. We provide a simple illustration of a Z-valuation. We show how we can use this representation to make decisions and answer questions. We show how to manipulate and combine multiple Z-valuations. We show the relationship between Z-numbers and linguistic summaries. Finally we provide for a representation of Z-valuations in terms of Dempster-Shafer belief structures, which makes use of type-2 fuzzy sets.

Keywords

Fuzzy Number Exponential Distribution Fuzzy Subset Possibility Distribution Ordered Weight Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ronald R. Yager
    • 1
  1. 1.Machine Intelligence InstituteIona College New RochelleUSA

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