Journal
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
Volume 27, Issue 3, Pages 259-278Publisher
WILEY
DOI: 10.1002/int.21521
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Funding
- Multidisciplinary University Research Initiative (MURI) [W911NF-09-1-0392]
- ONR [N000141010121]
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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 DempsterShafer belief structures, which makes use of type-2 fuzzy sets. (C) 2012 Wiley Periodicals, Inc.
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