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

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Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

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Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. SCOPIA Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa, Km. 7.5, 07122, Palma, Spain

    Sebastia Massanet, Juan Vicente Riera & Joan Torrens

Authors
  1. Sebastia Massanet
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  2. Juan Vicente Riera
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  3. Joan Torrens
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Corresponding author

Correspondence to Sebastia Massanet .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Massanet, S., Riera, J.V., Torrens, J. (2018). On the Aggregation of Zadeh’s Z-Numbers Based on Discrete Fuzzy Numbers. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_12

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_12

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  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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