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Possibility Distributions Generated by Intuitionistic \(\textsf {L}\)-Fuzzy Sets

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Rough Sets (IJCRS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12872))

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Abstract

In this work, we bridge possibility theory with intuitionistic L-fuzzy sets, by identifying a special class of possibility distributions corresponding to intuitionistic \(\textsf {L}\)-fuzzy sets based on a complete residuated lattice with an involution. Moreover, taking the \(\L \)ukasiewicz n-chains as structures of truth degrees, we propose an algorithm to compute the intuitionistic \(\textsf {L}\)-fuzzy set corresponding to a given possibility distribution, in case it exists.

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Notes

  1. 1.

    \(\textsf {L}\)-sets were introduced by Goguen [21] as generalizations of fuzzy sets.

  2. 2.

    We notice that, as in Definition 3, \(\mu \) and \(\nu \) have a symmetrical role, in the sense that \(\mu (x) \le \lnot \nu (x)\) is equivalent to \(\nu (x) \le \lnot \mu (x)\).

  3. 3.

    Additionally, given a intuitionistic \(\textsf {L}\)-fuzzy set \((\mu ,\nu )\), the value \(\pi _{(\mu , \nu )}(\omega )\) can be also understood as an answer to a bipolar fuzzy query given by \((\mu , \nu )\), where \(\mu \) and \(\nu \) respectively express positive and negative elastic constraints.

  4. 4.

    More in general, Proposition 4 holds when we consider complete residuated lattices with an involution and [0, 1] as support.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Stefania Boffa & Davide Ciucci

Authors
  1. Stefania Boffa
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  2. Davide Ciucci
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Correspondence to Stefania Boffa .

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Editors and Affiliations

  1. University of Winnipeg, Winnipeg, MB, Canada

    Sheela Ramanna

  2. Ghent University, Gent, Belgium

    Chris Cornelis

  3. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

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Boffa, S., Ciucci, D. (2021). Possibility Distributions Generated by Intuitionistic \(\textsf {L}\)-Fuzzy Sets. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds) Rough Sets. IJCRS 2021. Lecture Notes in Computer Science(), vol 12872. Springer, Cham. https://doi.org/10.1007/978-3-030-87334-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-87334-9_13

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