On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
The Dempster--Shafer calculus for statisticians
International Journal of Approximate Reasoning
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Classic Works of the Dempster-Shafer Theory of Belief Functions
Classic Works of the Dempster-Shafer Theory of Belief Functions
Information Sciences: an International Journal
Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice
Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice
IEEE Transactions on Fuzzy Systems
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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 Dempster–Shafer belief structures, which makes use of type-2 fuzzy sets. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.