On the Aggregation of Zadeh’s Z-Numbers Based on Discrete Fuzzy Numbers

  • Sebastia Massanet
  • Juan Vicente Riera
  • Joan Torrens
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 581)


The accurate modelling of natural language is one of the main goals in the theory of computing with words. Based on this idea, Zadeh in 2011, introduced the concept of Z-number which has a great potential not only from the theoretical point of view but also for many possible applications such as in economics, decision analysis, risk assessment, etc. Recently, the authors proposed a new vision of Zadeh’s Z-numbers based on discrete fuzzy numbers that simplifies the computations and maintains the flexibility of the original model from the linguistic point of view. Following with this novel interpretation, in this paper, algebraic structures in the set of Zadeh’s Z-numbers are studied. In this framework, we propose a method to construct aggregation functions from couples of discrete aggregation functions. In particular, t-norms and t-conorms are built. Finally, an application to reach a final decision on a decision making problem is given.


Zadeh’s Z-numbers Discrete fuzzy numbers Aggregation functions 



This paper has been partially supported by the Spanish Grant TIN2016-75404-P AEI/FEDER, UE.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Sebastia Massanet
    • 1
  • Juan Vicente Riera
    • 1
  • Joan Torrens
    • 1
  1. 1.SCOPIA Research Group, Department of Mathematics and Computer ScienceUniversity of the Balearic IslandsPalmaSpain

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