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On the Order-Compatibility of Fuzzy Logic Connectives on the Generated Clifford Poset

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

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Abstract

Fuzzy logic connectives have been order-theoretically explored in many recent works. Among them, Clifford’s relations, both the additive and multiplicative versions, are prominently employed for their generality as well as utility. While the algebraic properties of the original operation are preserved, its order-theoretic properties, viz., monotonicity, boundedness, etc., are not always preserved on the obtained Clifford poset. In this work, we characterize the necessary and sufficient conditions for these and examine the behaviour of certain fuzzy logic connectives on the induced Clifford posets.

Supported by SERB under the project MTR/2020/000506.

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Notes

  1. 1.

    Note that (ACR) is employed on fuzzy implications, which are mixed monotonic functions, to obtain the order. See Sect. 4.4 for more details.

  2. 2.

    It is worthy to highlight here that the conditional functional equations (CFEs) in Definition 3 are quite different from the usual CFEs in that we allow an argument to be substituted with another, albeit depending on the considered fixed triple and hence the nomenclature of being ‘localised’.

  3. 3.

    See Sect. 4.4 for more details.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Techology Hyderabad, Telangana, 502284, India

    Kavit Nanavati & Balasubramaniam Jayaram

Authors
  1. Kavit Nanavati
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  2. Balasubramaniam Jayaram
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Correspondence to Balasubramaniam Jayaram .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Nanavati, K., Jayaram, B. (2022). On the Order-Compatibility of Fuzzy Logic Connectives on the Generated Clifford Poset. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_58

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_58

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

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