Proceedings of ISP RAS

The Method of Converting an Expert Opinion to Z-number

E.A. Glukhoded (HSE, Moscow, Russia)
S.I. Smetanin (HSE, Moscow, Russia)


The concept of Z-numbers introduced by Zade in 2011 is discussed topically nowadays due to it aptitude to deal with nonlinearities and uncertainties whose are common in real life. It was a large step of representing fuzzy logic, however that numbers created much larger problems of how to calculate them or aggregate multiple numbers of that type. Z-numbers have a significant potential in the describing of the uncertainty of the human knowledge because both the expert assessment and the Z-number consists of restraint and reliability of the measured value. In this paper, a method of converting an expert opinion to Z-number is proposed according to set of specific questions. In addition, the approach to Z-numbers aggregation is introduced. Finally, submitted methods are demonstrated on a real example. The topicality of the research is developing a new algorithm and software (based on that development) which could help people make decision in a messy uncertainty with many parameters and factors that are also defined imprecisely. In this work, we present the research that is aimed to find the most efficient methods to operate them (aggregate, add, divide). Firstly, it is important to identify all existing methods of aggregating Z-numbers. Secondly, it is needed to invent new methods of how work with them. The most interesting techniques should be detailed and summarized. There is also a program that is developed to model the real-word task of decision-making.


Z-number, fuzzy measure, aggregation, expert opinion, fuzzy number


Proceedings of the Institute for System Programming, vol. 28, issue 3, 2016, pp. 7-20.

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2016-28(3)-1

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