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Proceedings of the Conference of the European Society for Fuzzy Logic and Technology

International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets

EUSFLAT 2017, IWIFSGN 2017: Advances in Fuzzy Logic and Technology 2017 pp 592–603Cite as

An Algorithm for Intermediate Quantifiers and the Graded Square of Opposition Towards Linguistic Description of Data

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

Abstract

The aim of this paper is to apply main theories of fuzzy natural logic together with fuzzy GUHA method for a linguistic characterization of relationships in data. Namely, we utilize the theory of intermediate quantifiers, which provides mathematical interpretation of natural language expressions describing quantity such as “Almost all”, “Few” etc., to describe relationships in data using vague terms that are natural in human expression. We provide an algorithm for computation of truth degrees of expressions containing such quantifiers. Moreover, we discuss some basic properties of intermediate quantifiers (contraries, contradictories, sub-contraries and sub-alterns), which formulate the graded Peterson’s square of opposition, and which can be used to infer new expressions from existing ones.

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Notes

  1. 1.

    Applying of delta connective in this definition we solve the problem \( \vdash \pmb {\lnot }(\forall x)(Bx\pmb {\Rightarrow }Ax)\equiv (\exists x)(Bx\mathop {\pmb { \& }}\nolimits \pmb {\lnot }Ax)\) then \(\mathscr {M}(\pmb {\lnot }\mathbf {A}\not \equiv \mathbf {O})=1\) since \(\mathbf {O}\mathrel {:=}\,(\exists x)(Bx\pmb {\wedge }\pmb {\lnot }Ax)\).

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Acknowledgment

The paper has been supported by the project “LQ1602 IT4Innovations excellence in science”.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling CE IT4Innovations, Division University of Ostrava, 30. Dubna 22, 701 03, Ostrava, Czech Republic

    Petra Murinová, Michal Burda & Viktor Pavliska

Authors
  1. Petra Murinová
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  2. Michal Burda
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  3. Viktor Pavliska
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Corresponding author

Correspondence to Petra Murinová .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Murinová, P., Burda, M., Pavliska, V. (2018). An Algorithm for Intermediate Quantifiers and the Graded Square of Opposition Towards Linguistic Description of Data. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_52

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  • DOI: https://doi.org/10.1007/978-3-319-66824-6_52

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