Relevance of Classes in a Fuzzy Partition. A Study from a Group of Aggregation Operators
This paper presents a study of the relevance property in a fuzzy partition from a fuzzy classification system. This study allows establishing a stopping criterion for the inclusion of a class in a fuzzy partition based on relevance. Such a criterion is constructed from a stable relationship on the commutative group formed by two new mappings (and the aggregation operators conjunctive and disjunctive) of the fuzzy classification system. The criterion is illustrated through an example on image analysis by the fuzzy c-means algorithm.
KeywordsRelevance Covering Overlap Classification Fuzzy partition
This research has been partially supported by the Government of Spain (grant TIN2015-66471-P), the Government of Madrid (grant S2013/ICE-2845), and Complutense University (UCM Research Group 910149).
- 12.Bustince, H., Barrenechea, E., Pagola, M., Fernández, J.: The notions of overlap and grouping functions. In: Saminger-Platz, S., Mesiar, R. (eds.) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory, Studies in Fuzziness and Soft Computing, vol. 336, pp. 137–156. Springer, Switzerland (2016). https://doi.org/10.1007/978-3-319-28808-6_8CrossRefGoogle Scholar
- 15.Qiao, J., Hu, B.Q.: On the migrativity of uninorms and nullnorms over overlap and grouping functions. Fuzzy Sets Syst. (2017). http://doi.org/10.1016/j.fss.2017.11.012
- 17.Sperber, D., Wilson, D.: Relevance: Communication and Cognition, 2nd edn. Blackwell Publishers Inc., Cambridge (1995)Google Scholar
- 19.Castiblanco, F., Gómez, D., Montero, J., Rodríguez, J.: Aggregation tools for the evaluation of classifications. In: 2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS). IEEE, Otsu, pp. 1–5 (2017)Google Scholar