Using L-fuzzy sets to introduce information theory into qualitative reasoning

  • Authors:

  • Francesc Prats;Llorenç Roselló;Mónica Sánchez;Núria Agell

  • Affiliations:

  • Universitat Politècnica de Catalunya, UPC-Barcelona Tech, Jordi Girona, 1-3, Barcelona, Spain;Universitat Politècnica de Catalunya, UPC-Barcelona Tech, Jordi Girona, 1-3, Barcelona, Spain;Universitat Politècnica de Catalunya, UPC-Barcelona Tech, Jordi Girona, 1-3, Barcelona, Spain;ESADE Business School, Universitat Ramon Llull, Av. Pedralbes 62, Barcelona, Spain

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2014

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Abstract

We formally construct the extended set of qualitative labels L over a well-ordered set. The qualitative descriptions of a given set are defined as L-fuzzy sets. In the case where the well-ordered set is finite, a distance between L-fuzzy sets is introduced based on the properties of the lattice L. The concept of the information contained in a qualitative label is introduced, leading to a formal definition of the entropy of an L-fuzzy set as a Lebesgue integral. In the discrete case, this integral becomes a weighted average of the information of the labels, corresponding to the Shannon entropy in information theory.