@article {COUSO201735, title = {Additive similarity and dissimilarity measures}, journal = {Fuzzy Sets and Systems}, volume = {322}, year = {2017}, note = {Theme: Preference and Similarity}, pages = {35 - 53}, abstract = {We develop a detailed formal study of the different variants of the notions of similarity and dissimilarity between fuzzy sets under the assumption of {\textquotedblleft}additivity{\textquotedblright}. A measure of (dis)similarity is said to be additive when it can be decomposed as the sum of the particular (dis)similarities of the compared memberships over the different elements of the universe. Some formal relations between existing formalizations of the notions of {\textquotedblleft}similarity{\textquotedblright} and {\textquotedblleft}dissimilarity{\textquotedblright} arise under this additional assumption. We conclude that, in this particular setting, one may basically distinguish between two main categories of comparison measures in the literature: those that depend on both the intersection and the difference of the compared items and those that only depend on their difference.}, keywords = {Comparison measure, Dissimilarity measure, Divergence measure, Measure of resemblance, Measure of similitude, Similarity measure}, issn = {0165-0114}, doi = {https://doi.org/10.1016/j.fss.2016.12.013}, url = {http://www.sciencedirect.com/science/article/pii/S0165011416304547}, author = {In{\'e}s Couso and Luciano S{\'a}nchez} } @article {COUSO2014114, title = {The notion of roughness of a fuzzy set}, journal = {Fuzzy Sets and Systems}, volume = {249}, year = {2014}, note = {Theme: Automata Theory and Algebra}, pages = {114 - 127}, abstract = {The roughness of a set (according to the notion introduced by Pawlak in 1991) can be regarded as the MZ-distance between its upper and the lower approximations. With this idea in mind, we have generalized Pawlak{\textquoteright}s definition, by replacing the MZ-distance by a general {\textquotedblleft}distance{\textquotedblright} measure. We also generalize the notion of roughness of fuzzy sets introduced by Huyhn and Nakamori in 2005.}, keywords = {Dissimilarity measure, Divergence measure, fuzzy set, Rough set, Roughness}, issn = {0165-0114}, doi = {https://doi.org/10.1016/j.fss.2014.02.013}, url = {http://www.sciencedirect.com/science/article/pii/S0165011414000657}, author = {In{\'e}s Couso and Laura Garrido and Luciano S{\'a}nchez} }