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Three-Valued Logics, Uncertainty Management and Rough Sets

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Transactions on Rough Sets XVII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 8375))

Abstract

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets.

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Authors and Affiliations

  1. DISCo, Università di Milano – Bicocca, Viale Sarca 336 – U14, 20126, Milano, Italy

    Davide Ciucci

  2. IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse cedex 4, France

    Didier Dubois

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  1. Davide Ciucci
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  2. Didier Dubois
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  1. Computational Intelligence Laboratory, ECE Department, University of Manitoba, MB R3T 5V6, Winnipeg, Canada

    James F. Peters

  2. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Ciucci, D., Dubois, D. (2014). Three-Valued Logics, Uncertainty Management and Rough Sets. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XVII. Lecture Notes in Computer Science, vol 8375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54756-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-54756-0_1

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