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Modeling and implementation of Z-number

Soft Computing, 2015
Computing with words provides symbolic and semantic methodology to deal with imprecise information associated with natural languages. It encapsulates various fuzzy logic techniques developed in past decades and formalizes them. Z-number is an emerging paradigm that has been utilized in computing with words among others.
Purvag Patel   +2 more
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On Z-valuations using Zadeh's Z-numbers

International Journal of Intelligent Systems, 2012
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.
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Total utility of Z-number

Applied Intelligence, 2017
Z-numbers, combined with “constraint” and “reliability”, has more power to express human knowledge. How to determine the ordering of Z-numbers and how to make a decision with Z-numbers are both meaningful and open issues. In this paper, a new notion of the total utility of Z-number is proposed to measure the total effects of a Z-number.
Bingyi Kang, Yong Deng 0001, Rehan Sadiq
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The arithmetic of continuous Z-numbers

Information Sciences, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafik A. Aliev   +2 more
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The arithmetic of multidimensional Z-number

Journal of Intelligent & Fuzzy Systems, 2018
The Z-number has become a new representation of evaluation information because of its superiority in describing reliability measure. Current studies focuses mainly on the unidimensional Z-number like Z = (about 25 min, usually). Studies on multidimensional cases have not been reported. However, because people often describe things from various aspects,
Kai-wen Shen   +2 more
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The arithmetic of discrete Z-numbers

Information Sciences, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafik A. Aliev   +2 more
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Hukuhara difference of Z-numbers

Information Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafik A. Aliev   +2 more
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A Note on the Maximum Number of Zeros of $$r(z) - \overline{z}$$ r ( z ) - z ¯

Computational Methods and Function Theory, 2015
\textit{D. Khavinson} and \textit{G. Neumann} [Proc. Am. Math. Soc. 134, No. 4, 1077--1085 (2006; Zbl 1090.30008)] showed that if \(r\) is a rational function of degree \(d\) greater than or equal to 2, then \(r(z)-\overline{z}\) has at most \(5d-5\) zeros. This result solved a problem in gravitational lensing.
Luce, Robert   +2 more
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Weyl numbers versus Z-Weyl numbers

Studia Mathematica, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carl, Bernd   +2 more
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Ordering of Z-numbers

AIP Conference Proceedings, 2017
The concept of Z-number which was introduced by Zadeh in 2010 has captured attention by many due to its enormous applications in the area of Computing with Words (CWW). A Z-number is an ordered pair of fuzzy numbers, (A, R), where A essentially plays the role of fuzzy restriction which is a real-valued uncertain variable and R is a measure of ...
Daud Mohamad   +2 more
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