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On Perception-based Logical Deduction with Fuzzy Inputs

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

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Abstract

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguistically expressed genuine logical implications. We analyze two variants of PbLD (original and balancing) that differ in the selection of fired IF-THEN rules. We concentrate on a situation when inputs into inference are fuzzy sets (fuzzy inputs). We study the conditions under which both variants fulfill the interpolativity property.

M. Štěpnička—This research was partially supported by the NPU II project LQ1602 “IT4Innovations excellence in science” provided by the MŠMT.

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Notes

  1. 1.

    We will call this degree a firing degree of the observation \(u_o\) in fuzzy rule \(\mathcal {R}_i\).

  2. 2.

    E.g., extremely small is more specific than small.

  3. 3.

    \({ LD}\) is viewed as a set, hence we omit multiple occurrences and each rule can be contained in \({ LD}\) only once.

  4. 4.

    Compared to (7), where a single fuzzy relation has to be a solution of the whole system, here not all rules are fired and each equation is solved separately.

  5. 5.

    When \(A_0\ne A_i\), not necessarily a single rule is fired. However, the original PbLD, compared to the fuzzy relational approach, notably reduces the number of fired rules.

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Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Antonín Dvořák & Martin Štěpnička

Authors
  1. Antonín Dvořák
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  2. Martin Štěpnička
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Corresponding author

Correspondence to Martin Štěpnička .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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Dvořák, A., Štěpnička, M. (2016). On Perception-based Logical Deduction with Fuzzy Inputs. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_40

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_40

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  • Online ISBN: 978-3-319-40581-0

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