TY - JOUR
T1 - Using L-fuzzy sets to introduce information theory into qualitative reasoning
AU - Prats, Francesc
AU - Roselló, Llorenç
AU - Sánchez, Mónica
AU - Agell, N.
N1 - Funding Information:
This research was partially supported by the SENSORIAL Research Project (TIN2010-20966-C02-01 and TIN2010-20966-C02-02), funded by the Spanish Ministry of Science and Information Technology. Partial support was also provided by a postdoctoral fellowship awarded to one of the authors at the ESADE Business School, with additional support from Ramon Llull University.
PY - 2014/2/1
Y1 - 2014/2/1
N2 - 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.
AB - 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.
KW - Information sciences
KW - L-fuzzy sets
KW - Measures of information
KW - Qualitative reasoning
UR - http://www.scopus.com/inward/record.url?scp=84888645657&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2013.06.013
DO - 10.1016/j.fss.2013.06.013
M3 - Article
AN - SCOPUS:84888645657
SN - 0165-0114
VL - 236
SP - 73
EP - 90
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -